Electromagnetic energy momentum thruster using tapered cavity resonator evanescent modes

ABSTRACT

An electromagnetic energy momentum thruster has a cavity resonator and an electromagnetic radiation source for emitting an electromagnetic wave in evanescence into the cavity resonator. The electromagnetic wave produces a greater electromagnetic field amplitude and a greater electromagnetic radiation pressure on a primary interior surface area of the cavity resonator than on a secondary interior surface area of the cavity resonator. The difference between the electromagnetic field amplitude on the primary interior surface area and on the secondary interior surface area of the cavity resonator forms a highly directional electromagnetic energy momentum tensor and provides a highly directional general relativistic metric tensor. As a result, a force is produced on the cavity resonator in the form of a thrust or an acceleration that propels the device in a direction substantially perpendicular to the primary interior surface area.

PRIORITY

This patent application claims priority from provisional U.S. patentapplication No. 62/629,106, filed Feb. 11, 2018, entitled,“ELECTROMAGNETIC ENERGY MOMENTUM THRUSTER USING TAPERED CAVITY RESONATOREVANESCENT MODES,” and naming Kyle Bernard Flanagan and Peter ClintonDohm as inventors, the disclosure of which is incorporated herein, inits entirety, by reference.

BACKGROUND

An electromagnetic energy momentum thruster, also known as a radiofrequency (RF) resonant cavity thruster or an EmDrive, is anelectromagnetic thruster comprising a cavity resonator and anelectromagnetic radiation source which produces a thrust from anelectromagnetic field inside the cavity resonator. Such electromagneticenergy momentum thrusters provide direct conversion of electrical energyto thrust without the use of a propellant.

Eagleworks Laboratories at NASA's Johnson Space Center led by Dr. Harold“Sonny” White has successfully tested an electromagnetic energy momentumthruster in a vacuum. Thrust measurement test results of the EmDrivewere presented at the 50^(th) AIAA/ASME/SAE/ASEE Joint PropulsionConference in Cleveland, Ohio on Jul. 28-30, 2014, and were published inAIAA Journal of Propulsion and Power in July 2017 in an articleentitled, “Measurement of Impulsive Thrust from a Closed Radio-FrequencyCavity in Vacuum”.

SUMMARY

Although electromagnetic energy momentum thrusters have been developed,many such devices known the inventors exhibit suboptimal propulsionefficiencies and produce low thrust. The suboptimal propulsionefficiencies of previously available electromagnetic energy momentumthrusters may be attributed to the inclusion of extraneous elementswithin the cavity resonator, suboptimal geometric designs, andinsufficient treatment of superconducting materials on the interiorsurface of the cavity resonator. These limitations of previouslyavailable electromagnetic energy momentum thrusters reduce thetransmission of electromagnetic energy due to absorption losses, andexhibit lower electromagnetic energy densities, electromagnetic momentumasymmetries, quality factors, propulsion efficiencies, and thrustcapabilities.

Provided herein are electromagnetic energy momentum thrusters whichexhibit high propulsion efficiencies and are configured to produce highthrust. In some embodiments, the shape of the cavity resonators providedherein enable an optimized RF tuning quality factor, and form largeelectric and magnetic field asymmetries. In some embodiments, the cavityresonators are designed with specific equations and boundary conditionswhich enable more efficient propulsion.

In some embodiments, the electromagnetic energy momentum thrustersprovided herein comprise a cavity resonator, which is configured forhighly efficient conversion of electrical energy to thrust or momentum.In some embodiments, at least one of a lack of extraneous interiorelements, the evacuation of the cavity resonator below a criticalpressure threshold, the cooling of the cavity resonator below a criticaltemperature threshold, and a superconductive coating within the cavityresonator enables such highly efficient propulsion. In some embodiments,the superconductive material within the cavity resonator is optimizedfor high quality factor. In some embodiments, the highly directionalelectromagnetic energy momentum tensor provides a highly directionalgeneral relativistic metric tensor and a corresponding free fallacceleration which is an equal and opposite reaction to an action ofthrust from the highly asymmetric electromagnetic radiation pressure.

Various embodiments include an electromagnetic energy momentum thrustercomprising: a cavity resonator forming a cavity having a base interiorsurface and a tapered interior surface, the tapered interior surfaceconverging to an apex point; and an electromagnetic radiation source incommunication with the cavity resonator, the electromagnetic radiationsource configured to emit an electromagnetic wave having a frequencybetween about 1.0 MHz to about 1000 THz into the cavity resonator.

In some embodiments, the electromagnetic radiation source is configuredto emit an electromagnetic wave into the cavity resonator having afrequency between about 10{circumflex over ( )}0 MHz to about10{circumflex over ( )}9 MHz. In some embodiments, the electromagneticradiation source is configured to emit an electromagnetic wave into thecavity resonator having a frequency of at least about 10{circumflex over( )}0 MHz. In some embodiments, the electromagnetic radiation source isconfigured to emit an electromagnetic wave into the cavity resonatorhaving a frequency of at most about 10{circumflex over ( )}9 MHz. Insome embodiments, the electromagnetic radiation source is configured toemit an electromagnetic wave into the cavity resonator having afrequency between about 10{circumflex over ( )}0 MHz to about10{circumflex over ( )}1 MHz, between about 10{circumflex over ( )}0 MHzto about 10{circumflex over ( )}2 MHz, between about 10{circumflex over( )}0 MHz to about 10{circumflex over ( )}3 MHz, between about10{circumflex over ( )}0 MHz to about 10{circumflex over ( )}4 MHz,between about 10{circumflex over ( )}0 MHz to about 10{circumflex over( )}5 MHz, between about 10{circumflex over ( )}0 MHz to about10{circumflex over ( )}6 MHz, between about 10{circumflex over ( )}0 MHzto about 10{circumflex over ( )}7 MHz, between about 10{circumflex over( )}0 MHz to about 10{circumflex over ( )}8 MHz, between about10{circumflex over ( )}0 MHz to about 10{circumflex over ( )}9 MHz,between about 10{circumflex over ( )}1 MHz to about 10{circumflex over( )}2 MHz, between about 10{circumflex over ( )}1 MHz to about10{circumflex over ( )}3 MHz, between about 10{circumflex over ( )}1 MHzto about 10{circumflex over ( )}4 MHz, between about 10{circumflex over( )}1 MHz to about 10{circumflex over ( )}5 MHz, between about10{circumflex over ( )}1 MHz to about 10{circumflex over ( )}6 MHz,between about 10{circumflex over ( )}1 MHz to about 10{circumflex over( )}7 MHz, between about 10{circumflex over ( )}1 MHz to about10{circumflex over ( )}8 MHz, between about 10{circumflex over ( )}1 MHzto about 10{circumflex over ( )}9 MHz, between about 10{circumflex over( )}2 MHz to about 10{circumflex over ( )}3 MHz, between about10{circumflex over ( )}2 MHz to about 10{circumflex over ( )}4 MHz,between about 10{circumflex over ( )}2 MHz to about 10{circumflex over( )}5 MHz, between about 10{circumflex over ( )}2 MHz to about10{circumflex over ( )}6 MHz, between about 10{circumflex over ( )}2 MHzto about 10{circumflex over ( )}7 MHz, between about 10{circumflex over( )}2 MHz to about 10{circumflex over ( )}8 MHz, between about10{circumflex over ( )}2 MHz to about 10{circumflex over ( )}9 MHz,between about 10{circumflex over ( )}3 MHz to about 10{circumflex over( )}4 MHz, between about 10{circumflex over ( )}3 MHz to about10{circumflex over ( )}5 MHz, between about 10{circumflex over ( )}3 MHzto about 10{circumflex over ( )}6 MHz, between about 10{circumflex over( )}3 MHz to about 10{circumflex over ( )}7 MHz, between about10{circumflex over ( )}3 MHz to about 10{circumflex over ( )}8 MHz,between about 10{circumflex over ( )}3 MHz to about 10{circumflex over( )}9 MHz, between about 10{circumflex over ( )}4 MHz to about10{circumflex over ( )}5 MHz, between about 10{circumflex over ( )}4 MHzto about 10{circumflex over ( )}6 MHz, between about 10{circumflex over( )}4 MHz to about 10{circumflex over ( )}7 MHz, between about10{circumflex over ( )}4 MHz to about 10{circumflex over ( )}8 MHz,between about 10{circumflex over ( )}4 MHz to about 10{circumflex over( )}9 MHz, between about 10{circumflex over ( )}5 MHz to about10{circumflex over ( )}6 MHz, between about 10{circumflex over ( )}5 MHzto about 10{circumflex over ( )}7 MHz, between about 10{circumflex over( )}5 MHz to about 10{circumflex over ( )}8 MHz, between about10{circumflex over ( )}5 MHz to about 10{circumflex over ( )}9 MHz,between about 10{circumflex over ( )}6 MHz to about 10{circumflex over( )}7 MHz, between about 10{circumflex over ( )}6 MHz to about10{circumflex over ( )}8 MHz, between about 10{circumflex over ( )}6 MHzto about 10{circumflex over ( )}9 MHz, between about 10{circumflex over( )}7 MHz to about 10{circumflex over ( )}8 MHz, between about10{circumflex over ( )}7 MHz to about 10{circumflex over ( )}9 MHz, orbetween about 10{circumflex over ( )}8 MHz to about 10{circumflex over( )}9 MHz. In some embodiments, the electromagnetic radiation source isconfigured to emit an electromagnetic wave into the cavity resonatorhaving a frequency of about 10{circumflex over ( )}0 MHz, about10{circumflex over ( )}1 MHz, about 10{circumflex over ( )}2 MHz, about10{circumflex over ( )}3 MHz, about 10{circumflex over ( )}4 MHz, about10{circumflex over ( )}5 MHz, about 10{circumflex over ( )}6 MHz, about10{circumflex over ( )}7 MHz, about 10{circumflex over ( )}8 MHz, orabout 10{circumflex over ( )}9 MHz, including increments therein.

In some embodiments, the electromagnetic radiation source is configuredto produce the frequency of the electromagnetic wave in evanescence sothat the electromagnetic wave has a maximum field amplitude and anasymptotic field amplitude, the maximum field amplitude being at, oradjacent to, the base interior surface, the asymptotic field amplitudebeing at, or adjacent to, one or both the tapered interior surface andthe apex point. In some embodiments, the electromagnetic radiationsource is configured to produce the frequency of the electromagneticwave in evanescence so that the electromagnetic wave has a maximum fieldamplitude and an asymptotic field amplitude, the maximum field amplitudebeing at, or adjacent to, one or both the tapered interior surface andthe apex point, and the asymptotic field amplitude being at, or adjacentto, the base interior surface.

In some embodiments, the cavity includes an overall interior surfacethat includes the base and tapered interior surfaces, substantially theentire overall interior surface being electrically conductive, whereinthe cavity resonator has a quality factor between about 10{circumflexover ( )}3 to about 10{circumflex over ( )}9. In some embodiments, thecavity resonator has a quality factor of at least about 10{circumflexover ( )}3. In some embodiments, the cavity resonator has a qualityfactor of at most about 10{circumflex over ( )}9. In some embodiments,the cavity resonator has a quality factor between about 10{circumflexover ( )}3 to about 10{circumflex over ( )}4, between about10{circumflex over ( )}3 to about 10{circumflex over ( )}5, betweenabout 10{circumflex over ( )}3 to about 10{circumflex over ( )}6,between about 10{circumflex over ( )}3 to about 10{circumflex over( )}7, between about 10{circumflex over ( )}3 to about 10{circumflexover ( )}8, between about 10{circumflex over ( )}3 to about10{circumflex over ( )}9, between about 10{circumflex over ( )}4 toabout 10{circumflex over ( )}5, between about 10{circumflex over ( )}4to about 10{circumflex over ( )}6, between about 10{circumflex over( )}4 to about 10{circumflex over ( )}7, between about 10{circumflexover ( )}4 to about 10{circumflex over ( )}8, between about10{circumflex over ( )}4 to about 10{circumflex over ( )}9, betweenabout 10{circumflex over ( )}5 to about 10{circumflex over ( )}6,between about 10{circumflex over ( )}5 to about 10{circumflex over( )}7, between about 10{circumflex over ( )}5 to about 10{circumflexover ( )}8, between about 10{circumflex over ( )}5 to about10{circumflex over ( )}9, between about 10{circumflex over ( )}6 toabout 10{circumflex over ( )}7, between about 10{circumflex over ( )}6to about 10{circumflex over ( )}8, between about 10{circumflex over( )}6 to about 10{circumflex over ( )}9, between about 10{circumflexover ( )}7 to about 10{circumflex over ( )}8, between about10{circumflex over ( )}7 to about 10{circumflex over ( )}9, or betweenabout 10{circumflex over ( )}8 to about 10{circumflex over ( )}9. Insome embodiments, the cavity resonator has a quality factor of about10{circumflex over ( )}3, about 10{circumflex over ( )}4, about10{circumflex over ( )}5, about 10{circumflex over ( )}6, about10{circumflex over ( )}7, about 10{circumflex over ( )}8, or about10{circumflex over ( )}9, including increments therein.

In some embodiments, the overall interior surface comprises aluminum,antimony, arsenic, barium, beryllium, bismuth, cadmium, calcium, carbon,chromium, cobalt, copper, gallium, gold, hydrogen, indium, iron,lanthanum, lead, lithium, magnesium, manganese, mercury, molybdenum,nickel, niobium, nitrogen, oxygen, palladium, phosphorus, platinum,scandium, silicon, silver, strontium, sulfur, tantalum, technetium, tin,titanium, tungsten, vanadium, yttrium, zinc, zirconium, or anycombination thereof.

In some embodiments, the cavity includes an overall interior surfacethat includes the base and tapered interior surfaces, substantially theentire overall interior surface being superconductive, wherein thecavity resonator has a quality factor between about 10{circumflex over( )}6 to about 10{circumflex over ( )}15. In some embodiments, thecavity resonator has a quality factor of at least about 10{circumflexover ( )}6. In some embodiments, the cavity resonator has a qualityfactor of at most about 10{circumflex over ( )}15. In some embodiments,the cavity resonator has a quality factor of between about 10{circumflexover ( )}6 to about 10{circumflex over ( )}7, between about10{circumflex over ( )}6 to about 10{circumflex over ( )}8, betweenabout 10{circumflex over ( )}6 to about 10{circumflex over ( )}9,between about 10{circumflex over ( )}6 to about 10{circumflex over( )}10, between about 10{circumflex over ( )}6 to about 10{circumflexover ( )}11, between about 10{circumflex over ( )}6 to about10{circumflex over ( )}12, between about 10{circumflex over ( )}6 toabout 10{circumflex over ( )}13, between about 10{circumflex over ( )}6to about 10{circumflex over ( )}14, between about 10{circumflex over( )}6 to about 10{circumflex over ( )}15, between about 10{circumflexover ( )}7 to about 10{circumflex over ( )}8, between about10{circumflex over ( )}7 to about 10{circumflex over ( )}9, betweenabout 10{circumflex over ( )}7 to about 10{circumflex over ( )}10,between about 10{circumflex over ( )}7 to about 10{circumflex over( )}11, between about 10{circumflex over ( )}7 to about 10{circumflexover ( )}12, between about 10{circumflex over ( )}7 to about10{circumflex over ( )}13, between about 10{circumflex over ( )}7 toabout 10{circumflex over ( )}14, between about 10{circumflex over ( )}7to about 10{circumflex over ( )}15, between about 10{circumflex over( )}8 to about 10{circumflex over ( )}9, between about 10{circumflexover ( )}8 to about 10{circumflex over ( )}10, between about10{circumflex over ( )}8 to about 10{circumflex over ( )}11, betweenabout 10{circumflex over ( )}8 to about 10{circumflex over ( )}12,between about 10{circumflex over ( )}8 to about 10{circumflex over( )}13, between about 10{circumflex over ( )}8 to about 10{circumflexover ( )}14, between about 10{circumflex over ( )}8 to about10{circumflex over ( )}15, between about 10{circumflex over ( )}9 toabout 10{circumflex over ( )}10, between about 10{circumflex over ( )}9to about 10{circumflex over ( )}11, between about 10{circumflex over( )}9 to about 10{circumflex over ( )}12, between about 10{circumflexover ( )}9 to about 10{circumflex over ( )}13, between about10{circumflex over ( )}9 to about 10{circumflex over ( )}14, betweenabout 10{circumflex over ( )}9 to about 10{circumflex over ( )}15,between about 10{circumflex over ( )}10 to about 10{circumflex over( )}11, between about 10{circumflex over ( )}10 to about 10{circumflexover ( )}12, between about 10{circumflex over ( )}10 to about10{circumflex over ( )}13, between about 10{circumflex over ( )}10 toabout 10{circumflex over ( )}14, between about 10{circumflex over ( )}10to about 10{circumflex over ( )}15, between about 10{circumflex over( )}11 to about 10{circumflex over ( )}12, between about 10{circumflexover ( )}11 to about 10{circumflex over ( )}13, between about10{circumflex over ( )}11 to about 10{circumflex over ( )}14, betweenabout 10{circumflex over ( )}11 to about 10{circumflex over ( )}15,between about 10{circumflex over ( )}12 to about 10{circumflex over( )}13, between about 10{circumflex over ( )}12 to about 10{circumflexover ( )}14, between about 10{circumflex over ( )}12 to about10{circumflex over ( )}15, between about 10{circumflex over ( )}13 toabout 10{circumflex over ( )}14, between about 10{circumflex over ( )}13to about 10{circumflex over ( )}15, or between about 10{circumflex over( )}14 to about 10{circumflex over ( )}15. In some embodiments, thecavity resonator has a quality factor of about 10{circumflex over ( )}6,about 10{circumflex over ( )}7, about 10{circumflex over ( )}8, about10{circumflex over ( )}9, about 10{circumflex over ( )}10, about10{circumflex over ( )}11, about 10{circumflex over ( )}12, about10{circumflex over ( )}13, about 10{circumflex over ( )}14, or about10{circumflex over ( )}15, including increments therein.

In some embodiments, the overall interior surface comprises aluminum,barium, beryllium, bismuth, cadmium, calcium, copper, gallium,gadolinium, germanium, lanthanum, lead, lithium, indium, mercury,molybdenum, niobium, nitrogen, osmium, oxygen, protactinium, rhenium,ruthenium, silicon, strontium, sulfur, tantalum, technetium, thallium,thorium, titanium, tin, vanadium, yttrium, zinc, zirconium, NbTi, PbMoS,V₃Ga, NbN, V₃Si, Nb₃Sn, Nb₃Al, Nb₃(AlGe), Nb₃Ge, Bi₂Sr₂CuO₆,Bi₂Sr₂CaCu₂O₈, Bi₂Sr₂Ca₂Cu₃O₁₀, YBa₂Cu₃O₇, YBa₂Cu₄O₈, Y₂Ba₄Cu₇O₁₅,Y₃Ba₅Cu₈O₁₈, Tl₂Ba₂CuO₆, Tl₂Ba₂CaCu₂O₈, Tl₂Ba₂Ca₂Cu₃O₁₀, TlBa₂Ca₃Cu₄O₁₁,HgBa₂CuO₄, HgBa₂CaCu₂O₆, HgBa₂Ca₂Cu₃O₈, or any combination thereof.

In some embodiments, the cavity is empty. In some embodiments, thecavity comprises a vacuum with a pressure between about 10{circumflexover ( )}-24 Torr to about 10{circumflex over ( )}3 Torr. In someembodiments, the cavity comprises a vacuum with a pressure of at leastabout 10{circumflex over ( )}-24 Torr. In some embodiments, the cavitycomprises a vacuum with a pressure of at most about 10{circumflex over( )}3 Torr. In some embodiments, the cavity comprises a vacuum with apressure between about 10{circumflex over ( )}-24 Torr to about10{circumflex over ( )}-21 Torr, between about 10{circumflex over( )}-24 Torr to about 10{circumflex over ( )}-18 Torr, between about10{circumflex over ( )}-24 Torr to about 10{circumflex over ( )}-15Torr, between about 10{circumflex over ( )}-24 Torr to about10{circumflex over ( )}-12 Torr, between about 10{circumflex over( )}-24 Torr to about 10{circumflex over ( )}-9 Torr, between about10{circumflex over ( )}-24 Torr to about 10{circumflex over ( )}-6 Torr,between about 10{circumflex over ( )}-24 Torr to about 10{circumflexover ( )}-3 Torr, between about 10{circumflex over ( )}-24 Torr to about1.0 Torr, between about 10{circumflex over ( )}-24 Torr to about10{circumflex over ( )}3 Torr, between about 10{circumflex over ( )}-21Torr to about 10{circumflex over ( )}-18 Torr, between about10{circumflex over ( )}-21 Torr to about 10{circumflex over ( )}-15Torr, between about 10{circumflex over ( )}-21 Torr to about10{circumflex over ( )}-12 Torr, between about 10{circumflex over( )}-21 Torr to about 10{circumflex over ( )}-9 Torr, between about10{circumflex over ( )}-21 Torr to about 10{circumflex over ( )}-6 Torr,between about 10{circumflex over ( )}-21 Torr to about 10{circumflexover ( )}-3 Torr, between about 10{circumflex over ( )}-21 Torr to about1.0 Torr, between about 10{circumflex over ( )}-21 Torr to about10{circumflex over ( )}3 Torr, between about 10{circumflex over ( )}-18Torr to about 10{circumflex over ( )}-15 Torr, between about10{circumflex over ( )}-18 Torr to about 10{circumflex over ( )}-12Torr, between about 10{circumflex over ( )}-18 Torr to about10{circumflex over ( )}-9 Torr, between about 10{circumflex over ( )}-18Torr to about 10{circumflex over ( )}-6 Torr, between about10{circumflex over ( )}-18 Torr to about 10{circumflex over ( )}-3 Torr,between about 10{circumflex over ( )}-18 Torr to about 1.0 Torr, betweenabout 10{circumflex over ( )}-18 Torr to about 10{circumflex over ( )}3Torr, between about 10{circumflex over ( )}-15 Torr to about10{circumflex over ( )}-12 Torr, between about 10{circumflex over( )}-15 Torr to about 10{circumflex over ( )}-9 Torr, between about10{circumflex over ( )}-15 Torr to about 10{circumflex over ( )}-6 Torr,between about 10{circumflex over ( )}-15 Torr to about 10{circumflexover ( )}-3 Torr, between about 10{circumflex over ( )}-15 Torr to about1.0 Torr, between about 10{circumflex over ( )}-15 Torr to about10{circumflex over ( )}3 Torr, between about 10{circumflex over ( )}-12Torr to about 10{circumflex over ( )}-9 Torr, between about10{circumflex over ( )}-12 Torr to about 10{circumflex over ( )}-6 Torr,between about 10{circumflex over ( )}-12 Torr to about 10{circumflexover ( )}-3 Torr, between about 10{circumflex over ( )}-12 Torr to about1.0 Torr, between about 10{circumflex over ( )}-12 Torr to about10{circumflex over ( )}3 Torr, between about 10{circumflex over ( )}-9Torr to about 10{circumflex over ( )}-6 Torr, between about10{circumflex over ( )}-9 Torr to about 10{circumflex over ( )}-3 Torr,between about 10{circumflex over ( )}-9 Torr to about 1.0 Torr, betweenabout 10{circumflex over ( )}-9 Torr to about 10{circumflex over ( )}3Torr, between about 10{circumflex over ( )}-6 Torr to about10{circumflex over ( )}-3 Torr, between about 10{circumflex over ( )}-6Torr to about 1.0 Torr, between about 10{circumflex over ( )}-6 Torr toabout 10{circumflex over ( )}3 Torr, between about 10{circumflex over( )}-3 Torr to about 1.0 Torr, between about 10{circumflex over ( )}-3Torr to about 10{circumflex over ( )}3 Torr, or between about 1.0 Torrto about 10{circumflex over ( )}3 Torr. In some embodiments, the cavitycomprises a vacuum with a pressure of about 10{circumflex over ( )}-24Torr, about 10{circumflex over ( )}-21 Torr, about 10{circumflex over( )}-18 Torr, about 10{circumflex over ( )}-15 Torr, about 10{circumflexover ( )}-12 Torr, about 10{circumflex over ( )}-9 Torr, about10{circumflex over ( )}-6 Torr, about 10{circumflex over ( )}-3 Torr,about 1.0 Torr, or about 10{circumflex over ( )}3 Torr, includingincrements therein.

In some embodiments, the cavity comprises a thermal reservoir with atemperature between about 10{circumflex over ( )}-3 Kelvin to about10{circumflex over ( )}3 Kelvin. In some embodiments, the cavitycomprises a thermal reservoir with a temperature of at least about10{circumflex over ( )}-3 Kelvin. In some embodiments, the cavitycomprises a thermal reservoir with a temperature of at most about10{circumflex over ( )}3 Kelvin. In some embodiments, the cavitycomprises a thermal reservoir with a temperature between about10{circumflex over ( )}-3 Kelvin to about 1 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 5 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 10 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 25 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 50 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 100 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 200 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 300 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 10{circumflex over ( )}3Kelvin, between about 1 Kelvin to about 5 Kelvin, between about 1 Kelvinto about 10 Kelvin, between about 1 Kelvin to about 25 Kelvin, betweenabout 1 Kelvin to about 50 Kelvin, between about 1 Kelvin to about 100Kelvin, between about 1 Kelvin to about 200 Kelvin, between about 1Kelvin to about 300 Kelvin, between about 1 Kelvin to about10{circumflex over ( )}3 Kelvin, between about 5 Kelvin to about 10Kelvin, between about 5 Kelvin to about 25 Kelvin, between about 5Kelvin to about 50 Kelvin, between about 5 Kelvin to about 100 Kelvin,between about 5 Kelvin to about 200 Kelvin, between about 5 Kelvin toabout 300 Kelvin, between about 5 Kelvin to about 10{circumflex over( )}3 Kelvin, between about 10 Kelvin to about 25 Kelvin, between about10 Kelvin to about 50 Kelvin, between about 10 Kelvin to about 100Kelvin, between about 10 Kelvin to about 200 Kelvin, between about 10Kelvin to about 300 Kelvin, between about 10 Kelvin to about10{circumflex over ( )}3 Kelvin, between about 25 Kelvin to about 50Kelvin, between about 25 Kelvin to about 100 Kelvin, between about 25Kelvin to about 200 Kelvin, between about 25 Kelvin to about 300 Kelvin,between about 25 Kelvin to about 10{circumflex over ( )}3 Kelvin,between about 50 Kelvin to about 100 Kelvin, between about 50 Kelvin toabout 200 Kelvin, between about 50 Kelvin to about 300 Kelvin, betweenabout 50 Kelvin to about 10{circumflex over ( )}3 Kelvin, between about100 Kelvin to about 200 Kelvin, between about 100 Kelvin to about 300Kelvin, between about 100 Kelvin to about 10{circumflex over ( )}3Kelvin, between about 200 Kelvin to about 300 Kelvin, between about 200Kelvin to about 10{circumflex over ( )}3 Kelvin, or between about 300Kelvin to about 10{circumflex over ( )}3 Kelvin. In some embodiments,the cavity comprises a thermal reservoir with a temperature of about10{circumflex over ( )}-3 Kelvin, about 1 Kelvin, about 5 Kelvin, about10 Kelvin, about 25 Kelvin, about 50 Kelvin, about 75 Kelvin, about 100Kelvin, about 150 Kelvin, about 200 Kelvin, about 300 Kelvin, or about10{circumflex over ( )}3 Kelvin, including increments therein.

In some embodiments, the electromagnetic wave comprises a transversemagnetic wave with a polar mode number of N1 and an azimuthal modenumber of N2, where N1 and N2 are integers from 0 to 1000, and N1 isgreater than or equal to N2. In some embodiments, the electromagneticwave comprises a transverse magnetic wave with a polar mode number of Nand an azimuthal mode number of 0, where N is an integer from 0 to 1000.In some embodiments, the electromagnetic wave comprises a transversemagnetic wave with a polar mode number of N and an azimuthal mode numberof N, where N is an integer from 0 to 1000. In some embodiments, theelectromagnetic wave comprises a transverse electric wave with a polarmode number of N1 and an azimuthal mode number of N2, where N1 and N2are an integers from 0 to 1000, and N1 is greater than or equal to N2.In some embodiments, the electromagnetic wave comprises a transverseelectric wave with a polar mode number of N and an azimuthal mode numberof 0, where N is an integer from 0 to 1000. In some embodiments, theelectromagnetic wave comprises a transverse electric wave with a polarmode number of N and an azimuthal mode number of N, where N is aninteger from 0 to 1000.

In some embodiments, the electromagnetic radiation source is locatedinside the cavity at, or adjacent to, a maximum field amplitude or anasymptotic field amplitude of the electromagnetic wave.

In some embodiments, the cavity has at least one of a width and a heightbetween about 10{circumflex over ( )}-9 meters to about 10{circumflexover ( )}3 meters. In some embodiments, the cavity has at least one of awidth and a height of at least about 10{circumflex over ( )}-9 meters.In some embodiments, the cavity has at least one of a width and a heightof at most about 10{circumflex over ( )}3 meters. In some embodiments,the cavity has at least one of a width and a height between about10{circumflex over ( )}-9 meters to about 10{circumflex over ( )}-6meters, between about 10{circumflex over ( )}-9 meters to about10{circumflex over ( )}-3 meters, between about 10{circumflex over( )}-9 meters to about 10{circumflex over ( )}-2 meters, between about10{circumflex over ( )}-9 meters to about 10{circumflex over ( )}-1meters, between about 10{circumflex over ( )}-9 meters to about 1.0meter, between about 10{circumflex over ( )}-9 meters to about10{circumflex over ( )}3 meters, between about 10{circumflex over ( )}-6meters to about 10{circumflex over ( )}-3 meters, between about10{circumflex over ( )}-6 meters to about 10{circumflex over ( )}-2meters, between about 10{circumflex over ( )}-6 meters to about10{circumflex over ( )}-1 meters, between about 10{circumflex over( )}-6 meters to about 1.0 meter, between about 10{circumflex over( )}-6 meters to about 10{circumflex over ( )}3 meters, between about10{circumflex over ( )}-3 meters to about 10{circumflex over ( )}-2meters, between about 10{circumflex over ( )}-3 meters to about10{circumflex over ( )}-1 meters, between about 10{circumflex over( )}-3 meters to about 1.0 meter, between about 10{circumflex over( )}-3 meters to about 10{circumflex over ( )}3 meters, between about10{circumflex over ( )}-2 meters to about 10{circumflex over ( )}-1meters, between about 10{circumflex over ( )}-2 meters to about 1.0meter, between about 10{circumflex over ( )}-2 meters to about10{circumflex over ( )}3 meters, between about 10{circumflex over ( )}-1meters to about 1.0 meter, between about 10{circumflex over ( )}-1meters to about 10{circumflex over ( )}3 meters, or between about 1.0meter to about 10{circumflex over ( )}3 meters. In some embodiments, thecavity has at least one of a width and a height of about 10{circumflexover ( )}-9 meters, about 10{circumflex over ( )}-6 meters, about10{circumflex over ( )}-3 meters, about 10{circumflex over ( )}-2meters, about 10{circumflex over ( )}-1 meters, about 1.0 meter, orabout 10{circumflex over ( )}3 meters, including increments therein.

In some embodiments, the tapered interior surface forms an apertureangle between about 5 degrees to about 175 degrees. In some embodiments,the tapered interior surface forms an aperture angle of at least about 5degrees. In some embodiments, the tapered interior surface forms anaperture angle of at most about 175 degrees. In some embodiments, thetapered interior surface forms an aperture angle between about 5 degreesto about 10 degrees, between about 5 degrees to about 20 degrees,between about 5 degrees to about 40 degrees, between about 5 degrees toabout 60 degrees, between about 5 degrees to about 80 degrees, betweenabout 5 degrees to about 100 degrees, between about 5 degrees to about120 degrees, between about 5 degrees to about 140 degrees, between about5 degrees to about 160 degrees, between about 5 degrees to about 175degrees, between about 10 degrees to about 20 degrees, between about 10degrees to about 40 degrees, between about 10 degrees to about 60degrees, between about 10 degrees to about 80 degrees, between about 10degrees to about 100 degrees, between about 10 degrees to about 120degrees, between about 10 degrees to about 140 degrees, between about 10degrees to about 160 degrees, between about 10 degrees to about 175degrees, between about 20 degrees to about 40 degrees, between about 20degrees to about 60 degrees, between about 20 degrees to about 80degrees, between about 20 degrees to about 100 degrees, between about 20degrees to about 120 degrees, between about 20 degrees to about 140degrees, between about 20 degrees to about 160 degrees, between about 20degrees to about 175 degrees, between about 40 degrees to about 60degrees, between about 40 degrees to about 80 degrees, between about 40degrees to about 100 degrees, between about 40 degrees to about 120degrees, between about 40 degrees to about 140 degrees, between about 40degrees to about 160 degrees, between about 40 degrees to about 175degrees, between about 60 degrees to about 80 degrees, between about 60degrees to about 100 degrees, between about 60 degrees to about 120degrees, between about 60 degrees to about 140 degrees, between about 60degrees to about 160 degrees, between about 60 degrees to about 175degrees, between about 80 degrees to about 100 degrees, between about 80degrees to about 120 degrees, between about 80 degrees to about 140degrees, between about 80 degrees to about 160 degrees, between about 80degrees to about 175 degrees, between about 100 degrees to about 120degrees, between about 100 degrees to about 140 degrees, between about100 degrees to about 160 degrees, between about 100 degrees to about 175degrees, between about 120 degrees to about 140 degrees, between about120 degrees to about 160 degrees, between about 120 degrees to about 175degrees, between about 140 degrees to about 160 degrees, between about140 degrees to about 175 degrees, or between about 160 degrees to about175 degrees. In some embodiments, the tapered interior surface forms anaperture angle of about 5 degrees, about 10 degrees, about 20 degrees,about 40 degrees, about 60 degrees, about 80 degrees, about 100 degrees,about 120 degrees, about 140 degrees, about 160 degrees, or about 175degrees, including increments therein.

In some embodiments, the cavity has a wall with a wall thickness betweenabout 10{circumflex over ( )}-9 meters to about 1.0 meter. In someembodiments, the cavity has a wall with a wall thickness of at leastabout 10{circumflex over ( )}-9 meters. In some embodiments, the cavityhas a wall with a wall thickness of at most about 1.0 meter. In someembodiments, the cavity has a wall with a wall thickness between about10{circumflex over ( )}-9 meters to about 10{circumflex over ( )}-6meters, between about 10{circumflex over ( )}-9 meters to about10{circumflex over ( )}-5 meters, between about 10{circumflex over( )}-9 meters to about 10{circumflex over ( )}-4 meters, between about10{circumflex over ( )}-9 meters to about 10{circumflex over ( )}-3meters, between about 10{circumflex over ( )}-9 meters to about 1.0meter, between about 10{circumflex over ( )}-6 meters to about10{circumflex over ( )}-5 meters, between about 10{circumflex over( )}-6 meters to about 10{circumflex over ( )}-4 meters, between about10{circumflex over ( )}-6 meters to about 10{circumflex over ( )}-3meters, between about 10{circumflex over ( )}-6 meters to about 1.0meter, between about 10{circumflex over ( )}-5 meters to about10{circumflex over ( )}-4 meters, between about 10{circumflex over( )}-5 meters to about 10{circumflex over ( )}-3 meters, between about10{circumflex over ( )}-5 meters to about 1.0 meter, between about10{circumflex over ( )}-4 meters to about 10{circumflex over ( )}-3meters, between about 10{circumflex over ( )}-4 meters to about 1.0meter, or between about 10{circumflex over ( )}-3 meters to about 1.0meter. In some embodiments, the cavity has a wall with a wall thicknessof about 10{circumflex over ( )}-9 meters, about 10{circumflex over( )}-6 meters, about 10{circumflex over ( )}-5 meters, about10{circumflex over ( )}-4 meters, about 10{circumflex over ( )}-3meters, or about 1.0 meter, including increments therein.

In some embodiments, the base interior surface is substantiallyelliptical. In some embodiments, the base interior surface issubstantially circular. In some embodiments, the base interior surfaceis substantially flat.

In some embodiments, the electromagnetic wave forms an electromagneticenergy momentum tensor with an amplitude maximum at, or adjacent to, thebase interior surface, which results in one or more of a metric tensorcurvature, a thrust, and an acceleration of the thruster. In someembodiments, the electromagnetic wave forms an electromagnetic energymomentum tensor with an amplitude maximum at, or adjacent to, one orboth the tapered interior surface and the apex point, which results inone or more of a metric tensor curvature, a thrust, and an accelerationof the thruster.

Another embodiment includes an electromagnetic energy momentum thrustercomprising: a cavity resonator forming a cavity having a base interiorsurface, a tapered interior surface, and a truncated interior surfaceopposing the base interior surface, the tapered interior surface beingbetween the base and truncated interior surfaces; and an electromagneticradiation source in communication with the cavity resonator, theelectromagnetic radiation source configured to emit an electromagneticwave having a frequency between about 1.0 MHz to about 1000 THz into thecavity resonator, the electromagnetic radiation source configured toproduce the electromagnetic wave in evanescence so that theelectromagnetic wave has a maximum field amplitude and an asymptoticfield amplitude.

In some embodiments, the electromagnetic radiation source is configuredto emit an electromagnetic wave into the cavity resonator having afrequency between about 10{circumflex over ( )}0 MHz to about10{circumflex over ( )}9 MHz. In some embodiments, the electromagneticradiation source is configured to emit an electromagnetic wave into thecavity resonator having a frequency of at least about 10{circumflex over( )}0 MHz. In some embodiments, the electromagnetic radiation source isconfigured to emit an electromagnetic wave into the cavity resonatorhaving a frequency of at most about 10{circumflex over ( )}9 MHz. Insome embodiments, the electromagnetic radiation source is configured toemit an electromagnetic wave into the cavity resonator having afrequency between about 10{circumflex over ( )}0 MHz to about10{circumflex over ( )}1 MHz, between about 10{circumflex over ( )}0 MHzto about 10{circumflex over ( )}2 MHz, between about 10{circumflex over( )}0 MHz to about 10{circumflex over ( )}3 MHz, between about10{circumflex over ( )}0 MHz to about 10{circumflex over ( )}4 MHz,between about 10{circumflex over ( )}0 MHz to about 10{circumflex over( )}5 MHz, between about 10{circumflex over ( )}0 MHz to about10{circumflex over ( )}6 MHz, between about 10{circumflex over ( )}0 MHzto about 10{circumflex over ( )}7 MHz, between about 10{circumflex over( )}0 MHz to about 10{circumflex over ( )}8 MHz, between about10{circumflex over ( )}0 MHz to about 10{circumflex over ( )}9 MHz,between about 10{circumflex over ( )}1 MHz to about 10{circumflex over( )}2 MHz, between about 10{circumflex over ( )}1 MHz to about10{circumflex over ( )}3 MHz, between about 10{circumflex over ( )}1 MHzto about 10{circumflex over ( )}4 MHz, between about 10{circumflex over( )}1 MHz to about 10{circumflex over ( )}5 MHz, between about10{circumflex over ( )}1 MHz to about 10{circumflex over ( )}6 MHz,between about 10{circumflex over ( )}1 MHz to about 10{circumflex over( )}7 MHz, between about 10{circumflex over ( )}1 MHz to about10{circumflex over ( )}8 MHz, between about 10{circumflex over ( )}1 MHzto about 10{circumflex over ( )}9 MHz, between about 10{circumflex over( )}2 MHz to about 10{circumflex over ( )}3 MHz, between about10{circumflex over ( )}2 MHz to about 10{circumflex over ( )}4 MHz,between about 10{circumflex over ( )}2 MHz to about 10{circumflex over( )}5 MHz, between about 10{circumflex over ( )}2 MHz to about10{circumflex over ( )}6 MHz, between about 10{circumflex over ( )}2 MHzto about 10{circumflex over ( )}7 MHz, between about 10{circumflex over( )}2 MHz to about 10{circumflex over ( )}8 MHz, between about10{circumflex over ( )}2 MHz to about 10{circumflex over ( )}9 MHz,between about 10{circumflex over ( )}3 MHz to about 10{circumflex over( )}4 MHz, between about 10{circumflex over ( )}3 MHz to about10{circumflex over ( )}5 MHz, between about 10{circumflex over ( )}3 MHzto about 10{circumflex over ( )}6 MHz, between about 10{circumflex over( )}3 MHz to about 10{circumflex over ( )}7 MHz, between about10{circumflex over ( )}3 MHz to about 10{circumflex over ( )}8 MHz,between about 10{circumflex over ( )}3 MHz to about 10{circumflex over( )}9 MHz, between about 10{circumflex over ( )}4 MHz to about10{circumflex over ( )}5 MHz, between about 10{circumflex over ( )}4 MHzto about 10{circumflex over ( )}6 MHz, between about 10{circumflex over( )}4 MHz to about 10{circumflex over ( )}7 MHz, between about10{circumflex over ( )}4 MHz to about 10{circumflex over ( )}8 MHz,between about 10{circumflex over ( )}4 MHz to about 10{circumflex over( )}9 MHz, between about 10{circumflex over ( )}5 MHz to about10{circumflex over ( )}6 MHz, between about 10{circumflex over ( )}5 MHzto about 10{circumflex over ( )}7 MHz, between about 10{circumflex over( )}5 MHz to about 10{circumflex over ( )}8 MHz, between about10{circumflex over ( )}5 MHz to about 10{circumflex over ( )}9 MHz,between about 10{circumflex over ( )}6 MHz to about 10{circumflex over( )}7 MHz, between about 10{circumflex over ( )}6 MHz to about10{circumflex over ( )}8 MHz, between about 10{circumflex over ( )}6 MHzto about 10{circumflex over ( )}9 MHz, between about 10{circumflex over( )}7 MHz to about 10{circumflex over ( )}8 MHz, between about10{circumflex over ( )}7 MHz to about 10{circumflex over ( )}9 MHz, orbetween about 10{circumflex over ( )}8 MHz to about 10{circumflex over( )}9 MHz. In some embodiments, the electromagnetic radiation source isconfigured to emit an electromagnetic wave into the cavity resonatorhaving a frequency of about 10{circumflex over ( )}0 MHz, about10{circumflex over ( )}1 MHz, about 10{circumflex over ( )}2 MHz, about10{circumflex over ( )}3 MHz, about 10{circumflex over ( )}4 MHz, about10{circumflex over ( )}5 MHz, about 10{circumflex over ( )}6 MHz, about10{circumflex over ( )}7 MHz, about 10{circumflex over ( )}8 MHz, orabout 10{circumflex over ( )}9 MHz, including increments therein.

In some embodiments, the maximum field amplitude is at, or adjacent to,the base interior surface, and the asymptotic field amplitude is at, oradjacent to, one or both the tapered interior surface and the truncatedinterior surface. In some embodiments, the maximum field amplitude isat, or adjacent to, one or both the tapered interior surface and thetruncated interior surface, and the asymptotic field amplitude is at, oradjacent to, the base interior surface.

In some embodiments, the cavity includes an overall interior surfacethat includes the base, tapered, and truncated interior surfaces,substantially the entire overall interior surface being electricallyconductive, wherein the cavity resonator has a quality factor betweenabout 10{circumflex over ( )}3 to about 10{circumflex over ( )}9. Insome embodiments, the cavity resonator has a quality factor of at leastabout 10{circumflex over ( )}3. In some embodiments, the cavityresonator has a quality factor of at most about 10{circumflex over( )}9. In some embodiments, the cavity resonator has a quality factorbetween about 10{circumflex over ( )}3 to about 10{circumflex over( )}4, between about 10{circumflex over ( )}3 to about 10{circumflexover ( )}5, between about 10{circumflex over ( )}3 to about10{circumflex over ( )}6, between about 10{circumflex over ( )}3 toabout 10{circumflex over ( )}7, between about 10{circumflex over ( )}3to about 10{circumflex over ( )}8, between about 10{circumflex over( )}3 to about 10{circumflex over ( )}9, between about 10{circumflexover ( )}4 to about 10{circumflex over ( )}5, between about10{circumflex over ( )}4 to about 10{circumflex over ( )}6, betweenabout 10{circumflex over ( )}4 to about 10{circumflex over ( )}7,between about 10{circumflex over ( )}4 to about 10{circumflex over( )}8, between about 10{circumflex over ( )}4 to about 10{circumflexover ( )}9, between about 10{circumflex over ( )}5 to about10{circumflex over ( )}6, between about 10{circumflex over ( )}5 toabout 10{circumflex over ( )}7, between about 10{circumflex over ( )}5to about 10{circumflex over ( )}8, between about 10{circumflex over( )}5 to about 10{circumflex over ( )}9, between about 10{circumflexover ( )}6 to about 10{circumflex over ( )}7, between about10{circumflex over ( )}6 to about 10{circumflex over ( )}8, betweenabout 10{circumflex over ( )}6 to about 10{circumflex over ( )}9,between about 10{circumflex over ( )}7 to about 10{circumflex over( )}8, between about 10{circumflex over ( )}7 to about 10{circumflexover ( )}9, or between about 10{circumflex over ( )}8 to about10{circumflex over ( )}9. In some embodiments, the cavity resonator hasa quality factor of about 10{circumflex over ( )}3, about 10{circumflexover ( )}4, about 10{circumflex over ( )}5, about 10{circumflex over( )}6, about 10{circumflex over ( )}7, about 10{circumflex over ( )}8,or about 10{circumflex over ( )}9, including increments therein.

In some embodiments, the overall interior surface comprises aluminum,antimony, arsenic, barium, beryllium, bismuth, cadmium, calcium, carbon,chromium, cobalt, copper, gallium, gold, hydrogen, indium, iron,lanthanum, lead, lithium, magnesium, manganese, mercury, molybdenum,nickel, niobium, nitrogen, oxygen, palladium, phosphorus, platinum,scandium, silicon, silver, strontium, sulfur, tantalum, technetium, tin,titanium, tungsten, vanadium, yttrium, zinc, zirconium, or anycombination thereof.

In some embodiments, the cavity includes an overall interior surfacethat includes the base, tapered, and/or truncated interior surfaces,substantially the entire overall interior surface being superconductive,wherein the cavity resonator has a quality factor between about10{circumflex over ( )}6 to about 10{circumflex over ( )}15. In someembodiments, the cavity resonator has a quality factor of at least about10{circumflex over ( )}6. In some embodiments, the cavity resonator hasa quality factor of at most about 10{circumflex over ( )}15. In someembodiments, the cavity resonator has a quality factor between about10{circumflex over ( )}6 to about 10{circumflex over ( )}7, betweenabout 10{circumflex over ( )}6 to about 10{circumflex over ( )}8,between about 10{circumflex over ( )}6 to about 10{circumflex over( )}9, between about 10{circumflex over ( )}6 to about 10{circumflexover ( )}10, between about 10{circumflex over ( )}6 to about10{circumflex over ( )}11, between about 10{circumflex over ( )}6 toabout 10{circumflex over ( )}12, between about 10{circumflex over ( )}6to about 10{circumflex over ( )}13, between about 10{circumflex over( )}6 to about 10{circumflex over ( )}14, between about 10{circumflexover ( )}6 to about 10{circumflex over ( )}15, between about10{circumflex over ( )}7 to about 10{circumflex over ( )}8, betweenabout 10{circumflex over ( )}7 to about 10{circumflex over ( )}9,between about 10{circumflex over ( )}7 to about 10{circumflex over( )}10, between about 10{circumflex over ( )}7 to about 10{circumflexover ( )}11, between about 10{circumflex over ( )}7 to about10{circumflex over ( )}12, between about 10{circumflex over ( )}7 toabout 10{circumflex over ( )}13, between about 10{circumflex over ( )}7to about 10{circumflex over ( )}14, between about 10{circumflex over( )}7 to about 10{circumflex over ( )}15, between about 10{circumflexover ( )}8 to about 10{circumflex over ( )}9, between about10{circumflex over ( )}8 to about 10{circumflex over ( )}10, betweenabout 10{circumflex over ( )}8 to about 10{circumflex over ( )}11,between about 10{circumflex over ( )}8 to about 10{circumflex over( )}12, between about 10{circumflex over ( )}8 to about 10{circumflexover ( )}13, between about 10{circumflex over ( )}8 to about10{circumflex over ( )}14, between about 10{circumflex over ( )}8 toabout 10{circumflex over ( )}15, between about 10{circumflex over ( )}9to about 10{circumflex over ( )}10, between about 10{circumflex over( )}9 to about 10{circumflex over ( )}11, between about 10{circumflexover ( )}9 to about 10{circumflex over ( )}12, between about10{circumflex over ( )}9 to about 10{circumflex over ( )}13, betweenabout 10{circumflex over ( )}9 to about 10{circumflex over ( )}14,between about 10{circumflex over ( )}9 to about 10{circumflex over( )}15, between about 10{circumflex over ( )}10 to about 10{circumflexover ( )}11, between about 10{circumflex over ( )}10 to about10{circumflex over ( )}12, between about 10{circumflex over ( )}10 toabout 10{circumflex over ( )}13, between about 10{circumflex over ( )}10to about 10{circumflex over ( )}14, between about 10{circumflex over( )}10 to about 10{circumflex over ( )}15, between about 10{circumflexover ( )}11 to about 10{circumflex over ( )}12, between about10{circumflex over ( )}11 to about 10{circumflex over ( )}13, betweenabout 10{circumflex over ( )}11 to about 10{circumflex over ( )}14,between about 10{circumflex over ( )}11 to about 10{circumflex over( )}15, between about 10{circumflex over ( )}12 to about 10{circumflexover ( )}13, between about 10{circumflex over ( )}12 to about10{circumflex over ( )}14, between about 10{circumflex over ( )}12 toabout 10{circumflex over ( )}15, between about 10{circumflex over ( )}13to about 10{circumflex over ( )}14, between about 10{circumflex over( )}13 to about 10{circumflex over ( )}15, or between about10{circumflex over ( )}14 to about 10{circumflex over ( )}15. In someembodiments, the cavity resonator has a quality factor of about10{circumflex over ( )}6, about 10{circumflex over ( )}7, about10{circumflex over ( )}8, about 10{circumflex over ( )}9, about10{circumflex over ( )}10, about 10{circumflex over ( )}11, about10{circumflex over ( )}12, about 10{circumflex over ( )}13, about10{circumflex over ( )}14, or about 10{circumflex over ( )}15, includingincrements therein.

In some embodiments, the overall interior surface comprises aluminum,barium, beryllium, bismuth, cadmium, calcium, copper, gallium,gadolinium, germanium, lanthanum, lead, lithium, indium, mercury,molybdenum, niobium, nitrogen, osmium, oxygen, protactinium, rhenium,ruthenium, silicon, strontium, sulfur, tantalum, technetium, thallium,thorium, titanium, tin, vanadium, yttrium, zinc, zirconium, NbTi, PbMoS,V₃Ga, NbN, V₃Si, Nb₃Sn, Nb₃Al, Nb₃(AlGe), Nb₃Ge, Bi₂Sr₂CuO₆,Bi₂Sr₂CaCu₂O₈, Bi₂Sr₂Ca₂Cu₃O₁₀, YBa₂Cu₃O₇, YBa₂Cu₄O₈, Y₂Ba₄Cu₇O₁₅,Y₃Ba₅Cu₈O₁₈, Tl₂Ba₂CuO₆, Tl₂Ba₂CaCu₂O₈, Tl₂Ba₂Ca₂Cu₃O₁₀, TlBa₂Ca₃Cu₄O₁₁,HgBa₂CuO₄, HgBa₂CaCu₂O₆, HgBa₂Ca₂Cu₃O₈, or any combination thereof.

In some embodiments, the cavity is empty. In some embodiments, thecavity comprises a vacuum with a pressure between about 10{circumflexover ( )}-24 Torr to about 10{circumflex over ( )}3 Torr. In someembodiments, the cavity comprises a vacuum with a pressure of at leastabout 10{circumflex over ( )}-24 Torr. In some embodiments, the cavitycomprises a vacuum with a pressure of at most about 10{circumflex over( )}3 Torr. In some embodiments, the cavity comprises a vacuum with apressure between about 10{circumflex over ( )}-24 Torr to about10{circumflex over ( )}-21 Torr, between about 10{circumflex over( )}-24 Torr to about 10{circumflex over ( )}-18 Torr, between about10{circumflex over ( )}-24 Torr to about 10{circumflex over ( )}-15Torr, between about 10{circumflex over ( )}-24 Torr to about10{circumflex over ( )}-12 Torr, between about 10{circumflex over( )}-24 Torr to about 10{circumflex over ( )}-9 Torr, between about10{circumflex over ( )}-24 Torr to about 10{circumflex over ( )}-6 Torr,between about 10{circumflex over ( )}-24 Torr to about 10{circumflexover ( )}-3 Torr, between about 10{circumflex over ( )}-24 Torr to about1.0 Torr, between about 10{circumflex over ( )}-24 Torr to about10{circumflex over ( )}3 Torr, between about 10{circumflex over ( )}-21Torr to about 10{circumflex over ( )}-18 Torr, between about10{circumflex over ( )}-21 Torr to about 10{circumflex over ( )}-15Torr, between about 10{circumflex over ( )}-21 Torr to about10{circumflex over ( )}-12 Torr, between about 10{circumflex over( )}-21 Torr to about 10{circumflex over ( )}-9 Torr, between about10{circumflex over ( )}-21 Torr to about 10{circumflex over ( )}-6 Torr,between about 10{circumflex over ( )}-21 Torr to about 10{circumflexover ( )}-3 Torr, between about 10{circumflex over ( )}-21 Torr to about1.0 Torr, between about 10{circumflex over ( )}-21 Torr to about10{circumflex over ( )}3 Torr, between about 10{circumflex over ( )}-18Torr to about 10{circumflex over ( )}-15 Torr, between about10{circumflex over ( )}-18 Torr to about 10{circumflex over ( )}-12Torr, between about 10{circumflex over ( )}-18 Torr to about10{circumflex over ( )}-9 Torr, between about 10{circumflex over ( )}-18Torr to about 10{circumflex over ( )}-6 Torr, between about10{circumflex over ( )}-18 Torr to about 10{circumflex over ( )}-3 Torr,between about 10{circumflex over ( )}-18 Torr to about 1.0 Torr, betweenabout 10{circumflex over ( )}-18 Torr to about 10{circumflex over ( )}3Torr, between about 10{circumflex over ( )}-15 Torr to about10{circumflex over ( )}-12 Torr, between about 10{circumflex over( )}-15 Torr to about 10{circumflex over ( )}-9 Torr, between about10{circumflex over ( )}-15 Torr to about 10{circumflex over ( )}-6 Torr,between about 10{circumflex over ( )}-15 Torr to about 10{circumflexover ( )}-3 Torr, between about 10{circumflex over ( )}-15 Torr to about1.0 Torr, between about 10{circumflex over ( )}-15 Torr to about10{circumflex over ( )}3 Torr, between about 10{circumflex over ( )}-12Torr to about 10{circumflex over ( )}-9 Torr, between about10{circumflex over ( )}-12 Torr to about 10{circumflex over ( )}-6 Torr,between about 10{circumflex over ( )}-12 Torr to about 10{circumflexover ( )}-3 Torr, between about 10{circumflex over ( )}-12 Torr to about1.0 Torr, between about 10{circumflex over ( )}-12 Torr to about10{circumflex over ( )}3 Torr, between about 10{circumflex over ( )}-9Torr to about 10{circumflex over ( )}-6 Torr, between about10{circumflex over ( )}-9 Torr to about 10{circumflex over ( )}-3 Torr,between about 10{circumflex over ( )}-9 Torr to about 1.0 Torr, betweenabout 10{circumflex over ( )}-9 Torr to about 10{circumflex over ( )}3Torr, between about 10{circumflex over ( )}-6 Torr to about10{circumflex over ( )}-3 Torr, between about 10{circumflex over ( )}-6Torr to about 1.0 Torr, between about 10{circumflex over ( )}-6 Torr toabout 10{circumflex over ( )}3 Torr, between about 10{circumflex over( )}-3 Torr to about 1.0 Torr, between about 10{circumflex over ( )}-3Torr to about 10{circumflex over ( )}3 Torr, or between about 1.0 Torrto about 10{circumflex over ( )}3 Torr. In some embodiments, the cavitycomprises a vacuum with a pressure of about 10{circumflex over ( )}-24Torr, about 10{circumflex over ( )}-21 Torr, about 10{circumflex over( )}-18 Torr, about 10{circumflex over ( )}-15 Torr, about 10{circumflexover ( )}-12 Torr, about 10{circumflex over ( )}-9 Torr, about10{circumflex over ( )}-6 Torr, about 10{circumflex over ( )}-3 Torr,about 1.0 Torr, or about 10{circumflex over ( )}3 Torr, includingincrements therein.

In some embodiments, the cavity comprises a thermal reservoir with atemperature between about 10{circumflex over ( )}-3 Kelvin about10{circumflex over ( )}3 Kelvin. In some embodiments, the cavitycomprises a thermal reservoir with a temperature of at least about10{circumflex over ( )}-3 Kelvin. In some embodiments, the cavitycomprises a thermal reservoir with a temperature of at most about10{circumflex over ( )}3 Kelvin. In some embodiments, the cavitycomprises a thermal reservoir with a temperature between about10{circumflex over ( )}-3 Kelvin to about 1 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 5 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 10 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 25 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 50 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 100 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 200 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 300 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 10{circumflex over ( )}3Kelvin, between about 1 Kelvin to about 5 Kelvin, between about 1 Kelvinto about 10 Kelvin, between about 1 Kelvin to about 25 Kelvin, betweenabout 1 Kelvin to about 50 Kelvin, between about 1 Kelvin to about 100Kelvin, between about 1 Kelvin to about 200 Kelvin, between about 1Kelvin to about 300 Kelvin, between about 1 Kelvin to about10{circumflex over ( )}3 Kelvin, between about 5 Kelvin to about 10Kelvin, between about 5 Kelvin to about 25 Kelvin, between about 5Kelvin to about 50 Kelvin, between about 5 Kelvin to about 100 Kelvin,between about 5 Kelvin to about 200 Kelvin, between about 5 Kelvin toabout 300 Kelvin, between about 5 Kelvin to about 10{circumflex over( )}3 Kelvin, between about 10 Kelvin to about 25 Kelvin, between about10 Kelvin to about 50 Kelvin, between about 10 Kelvin to about 100Kelvin, between about 10 Kelvin to about 200 Kelvin, between about 10Kelvin to about 300 Kelvin, between about 10 Kelvin to about10{circumflex over ( )}3 Kelvin, between about 25 Kelvin to about 50Kelvin, between about 25 Kelvin to about 100 Kelvin, between about 25Kelvin to about 200 Kelvin, between about 25 Kelvin to about 300 Kelvin,between about 25 Kelvin to about 10{circumflex over ( )}3 Kelvin,between about 50 Kelvin to about 100 Kelvin, between about 50 Kelvin toabout 200 Kelvin, between about 50 Kelvin to about 300 Kelvin, betweenabout 50 Kelvin to about 10{circumflex over ( )}3 Kelvin, between about100 Kelvin to about 200 Kelvin, between about 100 Kelvin to about 300Kelvin, between about 100 Kelvin to about 10{circumflex over ( )}3Kelvin, between about 200 Kelvin to about 300 Kelvin, between about 200Kelvin to about 10{circumflex over ( )}3 Kelvin, or between about 300Kelvin to about 10{circumflex over ( )}3 Kelvin. In some embodiments,the cavity comprises a thermal reservoir with a temperature of about10{circumflex over ( )}-3 Kelvin, about 1 Kelvin, about 5 Kelvin, about10 Kelvin, about 25 Kelvin, about 50 Kelvin, about 75 Kelvin, about 100Kelvin, about 150 Kelvin, about 200 Kelvin, about 300 Kelvin, or about10{circumflex over ( )}3 Kelvin, including increments therein.

In some embodiments, the electromagnetic wave comprises a transversemagnetic wave with a polar mode number of N1 and an azimuthal modenumber of N2, where N1 and N2 are an integers from 0 to 1000, and N1 isgreater than or equal to N2. In some embodiments, the electromagneticwave comprises a transverse magnetic wave with a polar mode number of Nand an azimuthal mode number of 0, where N is an integer from 0 to 1000.In some embodiments, the electromagnetic wave comprises a transversemagnetic wave with a polar mode number of N and an azimuthal mode numberof N, where N is an integer from 0 to 1000. In some embodiments, theelectromagnetic wave comprises a transverse electric wave with a polarmode number of N1 and an azimuthal mode number of N2, where N1 and N2are an integers from 0 to 1000, and N1 is greater than or equal to N2.In some embodiments, the electromagnetic wave comprises a transverseelectric wave with a polar mode number of N and an azimuthal mode numberof 0, where N is an integer from 0 to 1000. In some embodiments, theelectromagnetic wave comprises a transverse electric wave with a polarmode number of N and an azimuthal mode number of N, where N is aninteger from 0 to 1000.

In some embodiments, the electromagnetic radiation source is locatedinside the cavity at, or adjacent to, a maximum field amplitude or anasymptotic field amplitude of the electromagnetic wave.

In some embodiments, the cavity has at least one of a width and a heightbetween about 10{circumflex over ( )}-9 meters to about 10{circumflexover ( )}3 meters. In some embodiments, the cavity has at least one of awidth and a height of at least about 10{circumflex over ( )}-9 meters.In some embodiments, the cavity has at least one of a width and a heightof at most about 10{circumflex over ( )}3 meters. In some embodiments,the cavity has at least one of a width and a height between about10{circumflex over ( )}-9 meters to about 10{circumflex over ( )}-6meters, between about 10{circumflex over ( )}-9 meters to about10{circumflex over ( )}-3 meters, between about 10{circumflex over( )}-9 meters to about 10{circumflex over ( )}-2 meters, between about10{circumflex over ( )}-9 meters to about 10{circumflex over ( )}-1meters, between about 10{circumflex over ( )}-9 meters to about 1.0meter, between about 10{circumflex over ( )}-9 meters to about10{circumflex over ( )}3 meters, between about 10{circumflex over ( )}-6meters to about 10{circumflex over ( )}-3 meters, between about10{circumflex over ( )}-6 meters to about 10{circumflex over ( )}-2meters, between about 10{circumflex over ( )}-6 meters to about10{circumflex over ( )}-1 meters, between about 10{circumflex over( )}-6 meters to about 1.0 meter, between about 10{circumflex over( )}-6 meters to about 10{circumflex over ( )}3 meters, between about10{circumflex over ( )}-3 meters to about 10{circumflex over ( )}-2meters, between about 10{circumflex over ( )}-3 meters to about10{circumflex over ( )}-1 meters, between about 10{circumflex over( )}-3 meters to about 1.0 meter, between about 10{circumflex over( )}-3 meters to about 10{circumflex over ( )}3 meters, between about10{circumflex over ( )}-2 meters to about 10{circumflex over ( )}-1meters, between about 10{circumflex over ( )}-2 meters to about 1.0meter, between about 10{circumflex over ( )}-2 meters to about10{circumflex over ( )}3 meters, between about 10{circumflex over ( )}-1meters to about 1.0 meter, between about 10{circumflex over ( )}-1meters to about 10{circumflex over ( )}3 meters, or between about 1.0meter to about 10{circumflex over ( )}3 meters. In some embodiments, thecavity has at least one of a width and a height of about 10{circumflexover ( )}-9 meters, about 10{circumflex over ( )}-6 meters, about10{circumflex over ( )}-3 meters, about 10{circumflex over ( )}-2meters, about 10{circumflex over ( )}-1 meters, about 1.0 meter, orabout 10{circumflex over ( )}3 meters, including increments therein.

In some embodiments, the tapered interior surface forms an apertureangle between about 5 degrees to about 175 degrees. In some embodiments,the tapered interior surface forms an aperture angle of at least about 5degrees. In some embodiments, the tapered interior surface forms anaperture angle of at most about 175 degrees. In some embodiments, thetapered interior surface forms an aperture angle between about 5 degreesto about 10 degrees, between about 5 degrees to about 20 degrees,between about 5 degrees to about 40 degrees, between about 5 degrees toabout 60 degrees, between about 5 degrees to about 80 degrees, betweenabout 5 degrees to about 100 degrees, between about 5 degrees to about120 degrees, between about 5 degrees to about 140 degrees, between about5 degrees to about 160 degrees, between about 5 degrees to about 175degrees, between about 10 degrees to about 20 degrees, between about 10degrees to about 40 degrees, between about 10 degrees to about 60degrees, between about 10 degrees to about 80 degrees, between about 10degrees to about 100 degrees, between about 10 degrees to about 120degrees, between about 10 degrees to about 140 degrees, between about 10degrees to about 160 degrees, between about 10 degrees to about 175degrees, between about 20 degrees to about 40 degrees, between about 20degrees to about 60 degrees, between about 20 degrees to about 80degrees, between about 20 degrees to about 100 degrees, between about 20degrees to about 120 degrees, between about 20 degrees to about 140degrees, between about 20 degrees to about 160 degrees, between about 20degrees to about 175 degrees, between about 40 degrees to about 60degrees, between about 40 degrees to about 80 degrees, between about 40degrees to about 100 degrees, between about 40 degrees to about 120degrees, between about 40 degrees to about 140 degrees, between about 40degrees to about 160 degrees, between about 40 degrees to about 175degrees, between about 60 degrees to about 80 degrees, between about 60degrees to about 100 degrees, between about 60 degrees to about 120degrees, between about 60 degrees to about 140 degrees, between about 60degrees to about 160 degrees, between about 60 degrees to about 175degrees, between about 80 degrees to about 100 degrees, between about 80degrees to about 120 degrees, between about 80 degrees to about 140degrees, between about 80 degrees to about 160 degrees, between about 80degrees to about 175 degrees, between about 100 degrees to about 120degrees, between about 100 degrees to about 140 degrees, between about100 degrees to about 160 degrees, between about 100 degrees to about 175degrees, between about 120 degrees to about 140 degrees, between about120 degrees to about 160 degrees, between about 120 degrees to about 175degrees, between about 140 degrees to about 160 degrees, between about140 degrees to about 175 degrees, between or about 160 degrees to about175 degrees. In some embodiments, the tapered interior surface forms anaperture angle of about 5 degrees, about 10 degrees, about 20 degrees,about 40 degrees, about 60 degrees, about 80 degrees, about 100 degrees,about 120 degrees, about 140 degrees, about 160 degrees, or about 175degrees, including increments therein.

In some embodiments, the cavity has a wall with a wall thickness betweenabout 10{circumflex over ( )}-9 meters to about 1.0 meter. In someembodiments, the cavity has a wall with a wall thickness of at leastabout 10{circumflex over ( )}-9 meters. In some embodiments, the cavityhas a wall with a wall thickness of at most about 1.0 meter. In someembodiments, the cavity has a wall with a wall thickness between about10{circumflex over ( )}-9 meters to about 10{circumflex over ( )}-6meters, between about 10{circumflex over ( )}-9 meters to about10{circumflex over ( )}-5 meters, between about 10{circumflex over( )}-9 meters to about 10{circumflex over ( )}-4 meters, between about10{circumflex over ( )}-9 meters to about 10{circumflex over ( )}-3meters, between about 10{circumflex over ( )}-9 meters to about 1.0meter, between about 10{circumflex over ( )}-6 meters to about10{circumflex over ( )}-5 meters, between about 10{circumflex over( )}-6 meters to about 10{circumflex over ( )}-4 meters, between about10{circumflex over ( )}-6 meters to about 10{circumflex over ( )}-3meters, between about 10{circumflex over ( )}-6 meters to about 1.0meter, between about 10{circumflex over ( )}-5 meters to about10{circumflex over ( )}-4 meters, between about 10{circumflex over( )}-5 meters to about 10{circumflex over ( )}-3 meters, between about10{circumflex over ( )}-5 meters to about 1.0 meter, between about10{circumflex over ( )}-4 meters to about 10{circumflex over ( )}-3meters, between about 10{circumflex over ( )}-4 meters to about 1.0meter, or between about 10{circumflex over ( )}-3 meters to about 1.0meter. In some embodiments, the cavity has a wall with a wall thicknessof about 10{circumflex over ( )}-9 meters, about 10{circumflex over( )}-6 meters, about 10{circumflex over ( )}-5 meters, about10{circumflex over ( )}-4 meters, about 10{circumflex over ( )}-3meters, or about 1.0 meter, including increments therein.

In some embodiments, one or both the base interior surface and thetruncated interior surface of the cavity is substantially elliptical. Insome embodiments, one or both the base interior surface and thetruncated interior surface of the cavity is substantially circular. Insome embodiments, one or both the base interior surface and thetruncated interior surface of the cavity is substantially flat.

In some embodiments, the electromagnetic wave forms an electromagneticenergy momentum tensor with an amplitude maximum at, or adjacent to, thebase interior surface, which results in one or more of a metric tensorcurvature, a thrust, and an acceleration of the thruster. In someembodiments, the electromagnetic wave forms an electromagnetic energymomentum tensor with an amplitude maximum at, or adjacent to, one orboth the tapered interior surface and the truncated interior surface,which results in one or more of a metric tensor curvature, a thrust, andan acceleration of the thruster.

Another embodiment includes an electromagnetic energy momentum thrustercomprising: a cavity resonator forming a pyramidal cavity having a baseinterior surface and at least three tapered interior surfaces, thetapered interior surfaces converging to an apex point; and anelectromagnetic radiation source in communication with the cavityresonator, the electromagnetic radiation source configured to emit anelectromagnetic wave having a frequency between about 1.0 MHz to about1000 THz into the cavity resonator.

In some embodiments, the electromagnetic radiation source configured toemit an electromagnetic wave into the cavity resonator having afrequency between about 10{circumflex over ( )}0 MHz to about10{circumflex over ( )}9 MHz. In some embodiments, the electromagneticradiation source configured to emit an electromagnetic wave into thecavity resonator having a frequency of at least about 10{circumflex over( )}0 MHz. In some embodiments, the electromagnetic radiation sourceconfigured to emit an electromagnetic wave into the cavity resonatorhaving a frequency of at most about 10{circumflex over ( )}9 MHz. Insome embodiments, the electromagnetic radiation source configured toemit an electromagnetic wave into the cavity resonator having afrequency between about 10{circumflex over ( )}0 MHz to about10{circumflex over ( )}1 MHz, between about 10{circumflex over ( )}0 MHzto about 10{circumflex over ( )}2 MHz, between about 10{circumflex over( )}0 MHz to about 10{circumflex over ( )}3 MHz, between about10{circumflex over ( )}0 MHz to about 10{circumflex over ( )}4 MHz,between about 10{circumflex over ( )}0 MHz to about 10{circumflex over( )}5 MHz, between about 10{circumflex over ( )}0 MHz to about10{circumflex over ( )}6 MHz, between about 10{circumflex over ( )}0 MHzto about 10{circumflex over ( )}7 MHz, between about 10{circumflex over( )}0 MHz to about 10{circumflex over ( )}8 MHz, between about10{circumflex over ( )}0 MHz to about 10{circumflex over ( )}9 MHz,between about 10{circumflex over ( )}1 MHz to about 10{circumflex over( )}2 MHz, between about 10{circumflex over ( )}1 MHz to about10{circumflex over ( )}3 MHz, between about 10{circumflex over ( )}1 MHzto about 10{circumflex over ( )}4 MHz, between about 10{circumflex over( )}1 MHz to about 10{circumflex over ( )}5 MHz, between about10{circumflex over ( )}1 MHz to about 10{circumflex over ( )}6 MHz,between about 10{circumflex over ( )}1 MHz to about 10{circumflex over( )}7 MHz, between about 10{circumflex over ( )}1 MHz to about10{circumflex over ( )}8 MHz, between about 10{circumflex over ( )}1 MHzto about 10{circumflex over ( )}9 MHz, between about 10{circumflex over( )}2 MHz to about 10{circumflex over ( )}3 MHz, between about10{circumflex over ( )}2 MHz to about 10{circumflex over ( )}4 MHz,between about 10{circumflex over ( )}2 MHz to about 10{circumflex over( )}5 MHz, between about 10{circumflex over ( )}2 MHz to about10{circumflex over ( )}6 MHz, between about 10{circumflex over ( )}2 MHzto about 10{circumflex over ( )}7 MHz, between about 10{circumflex over( )}2 MHz to about 10{circumflex over ( )}8 MHz, between about10{circumflex over ( )}2 MHz to about 10{circumflex over ( )}9 MHz,between about 10{circumflex over ( )}3 MHz to about 10{circumflex over( )}4 MHz, between about 10{circumflex over ( )}3 MHz to about10{circumflex over ( )}5 MHz, between about 10{circumflex over ( )}3 MHzto about 10{circumflex over ( )}6 MHz, between about 10{circumflex over( )}3 MHz to about 10{circumflex over ( )}7 MHz, between about10{circumflex over ( )}3 MHz to about 10{circumflex over ( )}8 MHz,between about 10{circumflex over ( )}3 MHz to about 10{circumflex over( )}9 MHz, between about 10{circumflex over ( )}4 MHz to about10{circumflex over ( )}5 MHz, between about 10{circumflex over ( )}4 MHzto about 10{circumflex over ( )}6 MHz, between about 10{circumflex over( )}4 MHz to about 10{circumflex over ( )}7 MHz, between about10{circumflex over ( )}4 MHz to about 10{circumflex over ( )}8 MHz,between about 10{circumflex over ( )}4 MHz to about 10{circumflex over( )}9 MHz, between about 10{circumflex over ( )}5 MHz to about10{circumflex over ( )}6 MHz, between about 10{circumflex over ( )}5 MHzto about 10{circumflex over ( )}7 MHz, between about 10{circumflex over( )}5 MHz to about 10{circumflex over ( )}8 MHz, between about10{circumflex over ( )}5 MHz to about 10{circumflex over ( )}9 MHz,between about 10{circumflex over ( )}6 MHz to about 10{circumflex over( )}7 MHz, between about 10{circumflex over ( )}6 MHz to about10{circumflex over ( )}8 MHz, between about 10{circumflex over ( )}6 MHzto about 10{circumflex over ( )}9 MHz, between about 10{circumflex over( )}7 MHz to about 10{circumflex over ( )}8 MHz, between about10{circumflex over ( )}7 MHz to about 10{circumflex over ( )}9 MHz, orbetween about 10{circumflex over ( )}8 MHz to about 10{circumflex over( )}9 MHz. In some embodiments, the electromagnetic radiation sourceconfigured to emit an electromagnetic wave into the cavity resonatorhaving a frequency of about 10{circumflex over ( )}0 MHz, about10{circumflex over ( )}1 MHz, about 10{circumflex over ( )}2 MHz, about10{circumflex over ( )}3 MHz, about 10{circumflex over ( )}4 MHz, about10{circumflex over ( )}5 MHz, about 10{circumflex over ( )}6 MHz, about10{circumflex over ( )}7 MHz, about 10{circumflex over ( )}8 MHz, orabout 10{circumflex over ( )}9 MHz, including increments therein.

In some embodiments, the electromagnetic radiation source is configuredto produce the frequency of the electromagnetic wave in evanescence sothat the electromagnetic wave has a maximum field amplitude and anasymptotic field amplitude, the maximum field amplitude being at, oradjacent to, the base interior surface, the asymptotic field amplitudebeing at, or adjacent to, one or more of the at least three taperedinterior surfaces and the apex point. In some embodiments, theelectromagnetic radiation source is configured to produce the frequencyof the electromagnetic wave in evanescence so that the electromagneticwave has a maximum field amplitude and an asymptotic field amplitude,the maximum field amplitude being at, or adjacent to, one or more of theat least three tapered interior surfaces and the apex point, and theasymptotic field amplitude being at, or adjacent to, the base interiorsurface.

In some embodiments, the cavity includes an overall interior surfacethat includes the base and tapered interior surfaces, substantially theentire overall interior surface being electrically conductive, whereinthe cavity resonator has a quality factor between about 10{circumflexover ( )}3 to about 10{circumflex over ( )}9. In some embodiments, thecavity resonator has a quality factor of at least about 10{circumflexover ( )}3. In some embodiments, the cavity resonator has a qualityfactor of at most about 10{circumflex over ( )}9. In some embodiments,the cavity resonator has a quality factor between about 10{circumflexover ( )}3 to about 10{circumflex over ( )}4, between about10{circumflex over ( )}3 to about 10{circumflex over ( )}5, betweenabout 10{circumflex over ( )}3 to about 10{circumflex over ( )}6,between about 10{circumflex over ( )}3 to about 10{circumflex over( )}7, between about 10{circumflex over ( )}3 to about 10{circumflexover ( )}8, between about 10{circumflex over ( )}3 to about10{circumflex over ( )}9, between about 10{circumflex over ( )}4 toabout 10{circumflex over ( )}5, between about 10{circumflex over ( )}4to about 10{circumflex over ( )}6, between about 10{circumflex over( )}4 to about 10{circumflex over ( )}7, between about 10{circumflexover ( )}4 to about 10{circumflex over ( )}8, between about10{circumflex over ( )}4 to about 10{circumflex over ( )}9, betweenabout 10{circumflex over ( )}5 to about 10{circumflex over ( )}6,between about 10{circumflex over ( )}5 to about 10{circumflex over( )}7, between about 10{circumflex over ( )}5 to about 10{circumflexover ( )}8, between about 10{circumflex over ( )}5 to about10{circumflex over ( )}9, between about 10{circumflex over ( )}6 toabout 10{circumflex over ( )}7, between about 10{circumflex over ( )}6to about 10{circumflex over ( )}8, between about 10{circumflex over( )}6 to about 10{circumflex over ( )}9, between about 10{circumflexover ( )}7 to about 10{circumflex over ( )}8, between about10{circumflex over ( )}7 to about 10{circumflex over ( )}9, or betweenabout 10{circumflex over ( )}8 to about 10{circumflex over ( )}9. Insome embodiments, the cavity resonator has a quality factor of about10{circumflex over ( )}3, about 10{circumflex over ( )}4, about10{circumflex over ( )}5, about 10{circumflex over ( )}6, about10{circumflex over ( )}7, about 10{circumflex over ( )}8, or about10{circumflex over ( )}9, including increments therein.

In some embodiments, the overall interior surface comprises aluminum,antimony, arsenic, barium, beryllium, bismuth, cadmium, calcium, carbon,chromium, cobalt, copper, gallium, gold, hydrogen, indium, iron,lanthanum, lead, lithium, magnesium, manganese, mercury, molybdenum,nickel, niobium, nitrogen, oxygen, palladium, phosphorus, platinum,scandium, silicon, silver, strontium, sulfur, tantalum, technetium, tin,titanium, tungsten, vanadium, yttrium, zinc, zirconium, or anycombination thereof.

In some embodiments, the cavity includes an overall interior surfacethat includes the base and tapered interior surfaces, substantially theentire overall interior surface being superconductive, wherein thecavity resonator has a quality factor between about 10{circumflex over( )}6 to about 10{circumflex over ( )}15. In some embodiments, thecavity resonator has a quality factor of at least about 10{circumflexover ( )}6. In some embodiments, the cavity resonator has a qualityfactor of at most about 10{circumflex over ( )}15. In some embodiments,the cavity resonator has a quality factor between about 10{circumflexover ( )}6 to about 10{circumflex over ( )}7, between about10{circumflex over ( )}6 to about 10{circumflex over ( )}8, betweenabout 10{circumflex over ( )}6 to about 10{circumflex over ( )}9,between about 10{circumflex over ( )}6 to about 10{circumflex over( )}10, between about 10{circumflex over ( )}6 to about 10{circumflexover ( )}11, between about 10{circumflex over ( )}6 to about10{circumflex over ( )}12, between about 10{circumflex over ( )}6 toabout 10{circumflex over ( )}13, between about 10{circumflex over ( )}6to about 10{circumflex over ( )}14, between about 10{circumflex over( )}6 to about 10{circumflex over ( )}15, between about 10{circumflexover ( )}7 to about 10{circumflex over ( )}8, between about10{circumflex over ( )}7 to about 10{circumflex over ( )}9, betweenabout 10{circumflex over ( )}7 to about 10{circumflex over ( )}10,between about 10{circumflex over ( )}7 to about 10{circumflex over( )}11, between about 10{circumflex over ( )}7 to about 10{circumflexover ( )}12, between about 10{circumflex over ( )}7 to about10{circumflex over ( )}13, between about 10{circumflex over ( )}7 toabout 10{circumflex over ( )}14, between about 10{circumflex over ( )}7to about 10{circumflex over ( )}15, between about 10{circumflex over( )}8 to about 10{circumflex over ( )}9, between about 10{circumflexover ( )}8 to about 10{circumflex over ( )}10, between about10{circumflex over ( )}8 to about 10{circumflex over ( )}11, betweenabout 10{circumflex over ( )}8 to about 10{circumflex over ( )}12,between about 10{circumflex over ( )}8 to about 10{circumflex over( )}13, between about 10{circumflex over ( )}8 to about 10{circumflexover ( )}14, between about 10{circumflex over ( )}8 to about10{circumflex over ( )}15, between about 10{circumflex over ( )}9 toabout 10{circumflex over ( )}10, between about 10{circumflex over ( )}9to about 10{circumflex over ( )}11, between about 10{circumflex over( )}9 to about 10{circumflex over ( )}12, between about 10{circumflexover ( )}9 to about 10{circumflex over ( )}13, between about10{circumflex over ( )}9 to about 10{circumflex over ( )}14, betweenabout 10{circumflex over ( )}9 to about 10{circumflex over ( )}15,between about 10{circumflex over ( )}10 to about 10{circumflex over( )}11, between about 10{circumflex over ( )}10 to about 10{circumflexover ( )}12, between about 10{circumflex over ( )}10 to about10{circumflex over ( )}13, between about 10{circumflex over ( )}10 toabout 10{circumflex over ( )}14, between about 10{circumflex over ( )}10to about 10{circumflex over ( )}15, between about 10{circumflex over( )}11 to about 10{circumflex over ( )}12, between about 10{circumflexover ( )}11 to about 10{circumflex over ( )}13, between about10{circumflex over ( )}11 to about 10{circumflex over ( )}14, betweenabout 10{circumflex over ( )}11 to about 10{circumflex over ( )}15,between about 10{circumflex over ( )}12 to about 10{circumflex over( )}13, between about 10{circumflex over ( )}12 to about 10{circumflexover ( )}14, between about 10{circumflex over ( )}12 to about10{circumflex over ( )}15, between about 10{circumflex over ( )}13 toabout 10{circumflex over ( )}14, between about 10{circumflex over ( )}13to about 10{circumflex over ( )}15, or between about 10{circumflex over( )}14 to about 10{circumflex over ( )}15. In some embodiments, thecavity resonator has a quality factor of about 10{circumflex over ( )}6,about 10{circumflex over ( )}7, about 10{circumflex over ( )}8, about10{circumflex over ( )}9, about 10{circumflex over ( )}10, about10{circumflex over ( )}11, about 10{circumflex over ( )}12, about10{circumflex over ( )}13, about 10{circumflex over ( )}14, or about10{circumflex over ( )}15, including increments therein.

In some embodiments, the overall interior surface comprises aluminum,barium, beryllium, bismuth, cadmium, calcium, copper, gallium,gadolinium, germanium, lanthanum, lead, lithium, indium, mercury,molybdenum, niobium, nitrogen, osmium, oxygen, protactinium, rhenium,ruthenium, silicon, strontium, sulfur, tantalum, technetium, thallium,thorium, titanium, tin, vanadium, yttrium, zinc, zirconium, NbTi, PbMoS,V₃Ga, NbN, V₃Si, Nb₃Sn, Nb₃Al, Nb₃(AlGe), Nb₃Ge, Bi₂Sr₂CuO₆,Bi₂Sr₂CaCu₂O₈, Bi₂Sr₂Ca₂Cu₃O₁₀, YBa₂Cu₃O₇, YBa₂Cu₄O₈, Y₂Ba₄Cu₇O₁₅,Y₃Ba₅Cu₈O₁₈, Tl₂Ba₂CuO₆, Tl₂Ba₂CaCu₂O₈, Tl₂Ba₂Ca₂Cu₃O₁₀, TlBa₂Ca₃Cu₄O₁₁,HgBa₂CuO₄, HgBa₂CaCu₂O₆, HgBa₂Ca₂Cu₃O₈, or any combination thereof.

In some embodiments, the cavity is empty. In some embodiments, thecavity comprises a vacuum with a pressure between about 10{circumflexover ( )}-24 Torr to about 10{circumflex over ( )}3 Torr. In someembodiments, the cavity comprises a vacuum with a pressure of at leastabout 10{circumflex over ( )}-24 Torr. In some embodiments, the cavitycomprises a vacuum with a pressure of at most about 10{circumflex over( )}3 Torr. In some embodiments, the cavity comprises a vacuum with apressure between about 10{circumflex over ( )}-24 Torr to about10{circumflex over ( )}-21 Torr, between about 10{circumflex over( )}-24 Torr to about 10{circumflex over ( )}-18 Torr, between about10{circumflex over ( )}-24 Torr to about 10{circumflex over ( )}-15Torr, between about 10{circumflex over ( )}-24 Torr to about10{circumflex over ( )}-12 Torr, between about 10{circumflex over( )}-24 Torr to about 10{circumflex over ( )}-9 Torr, between about10{circumflex over ( )}-24 Torr to about 10{circumflex over ( )}-6 Torr,between about 10{circumflex over ( )}-24 Torr to about 10{circumflexover ( )}-3 Torr, between about 10{circumflex over ( )}-24 Torr to about1.0 Torr, between about 10{circumflex over ( )}-24 Torr to about10{circumflex over ( )}3 Torr, between about 10{circumflex over ( )}-21Torr to about 10{circumflex over ( )}-18 Torr, between about10{circumflex over ( )}-21 Torr to about 10{circumflex over ( )}-15Torr, between about 10{circumflex over ( )}-21 Torr to about10{circumflex over ( )}-12 Torr, between about 10{circumflex over( )}-21 Torr to about 10{circumflex over ( )}-9 Torr, between about10{circumflex over ( )}-21 Torr to about 10{circumflex over ( )}-6 Torr,between about 10{circumflex over ( )}-21 Torr to about 10{circumflexover ( )}-3 Torr, between about 10{circumflex over ( )}-21 Torr to about1.0 Torr, between about 10{circumflex over ( )}-21 Torr to about10{circumflex over ( )}3 Torr, between about 10{circumflex over ( )}-18Torr to about 10{circumflex over ( )}-15 Torr, between about10{circumflex over ( )}-18 Torr to about 10{circumflex over ( )}-12Torr, between about 10{circumflex over ( )}-18 Torr to about10{circumflex over ( )}-9 Torr, between about 10{circumflex over ( )}-18Torr to about 10{circumflex over ( )}-6 Torr, between about10{circumflex over ( )}-18 Torr to about 10{circumflex over ( )}-3 Torr,between about 10{circumflex over ( )}-18 Torr to about 1.0 Torr, betweenabout 10{circumflex over ( )}-18 Torr to about 10{circumflex over ( )}3Torr, between about 10{circumflex over ( )}-15 Torr to about10{circumflex over ( )}-12 Torr, between about 10{circumflex over( )}-15 Torr to about 10{circumflex over ( )}-9 Torr, between about10{circumflex over ( )}-15 Torr to about 10{circumflex over ( )}-6 Torr,between about 10{circumflex over ( )}-15 Torr to about 10{circumflexover ( )}-3 Torr, between about 10{circumflex over ( )}-15 Torr to about1.0 Torr, between about 10{circumflex over ( )}-15 Torr to about10{circumflex over ( )}3 Torr, between about 10{circumflex over ( )}-12Torr to about 10{circumflex over ( )}-9 Torr, between about10{circumflex over ( )}-12 Torr to about 10{circumflex over ( )}-6 Torr,between about 10{circumflex over ( )}-12 Torr to about 10{circumflexover ( )}-3 Torr, between about 10{circumflex over ( )}-12 Torr to about1.0 Torr, between about 10{circumflex over ( )}-12 Torr to about10{circumflex over ( )}3 Torr, between about 10{circumflex over ( )}-9Torr to about 10{circumflex over ( )}-6 Torr, between about10{circumflex over ( )}-9 Torr to about 10{circumflex over ( )}-3 Torr,between about 10{circumflex over ( )}-9 Torr to about 1.0 Torr, betweenabout 10{circumflex over ( )}-9 Torr to about 10{circumflex over ( )}3Torr, between about 10{circumflex over ( )}-6 Torr to about10{circumflex over ( )}-3 Torr, between about 10{circumflex over ( )}-6Torr to about 1.0 Torr, between about 10{circumflex over ( )}-6 Torr toabout 10{circumflex over ( )}3 Torr, between about 10{circumflex over( )}-3 Torr to about 1.0 Torr, between about 10{circumflex over ( )}-3Torr to about 10{circumflex over ( )}3 Torr, or between about 1.0 Torrto about 10{circumflex over ( )}3 Torr. In some embodiments, the cavitycomprises a vacuum with a pressure of about 10{circumflex over ( )}-24Torr, about 10{circumflex over ( )}-21 Torr, about 10{circumflex over( )}-18 Torr, about 10{circumflex over ( )}-15 Torr, about 10{circumflexover ( )}-12 Torr, about 10{circumflex over ( )}-9 Torr, about10{circumflex over ( )}-6 Torr, about 10{circumflex over ( )}-3 Torr,about 1.0 Torr, or about 10{circumflex over ( )}3 Torr, includingincrements therein.

In some embodiments, the cavity comprises a thermal reservoir with atemperature between about 10{circumflex over ( )}-3 Kelvin about10{circumflex over ( )}3 Kelvin. In some embodiments, the cavitycomprises a thermal reservoir with a temperature of at least about10{circumflex over ( )}-3 Kelvin. In some embodiments, the cavitycomprises a thermal reservoir with a temperature of at most about10{circumflex over ( )}3 Kelvin. In some embodiments, the cavitycomprises a thermal reservoir with a temperature between about10{circumflex over ( )}-3 Kelvin to about 1 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 5 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 10 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 25 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 50 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 100 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 200 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 300 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 10{circumflex over ( )}3Kelvin, between about 1 Kelvin to about 5 Kelvin, between about 1 Kelvinto about 10 Kelvin, between about 1 Kelvin to about 25 Kelvin, betweenabout 1 Kelvin to about 50 Kelvin, between about 1 Kelvin to about 100Kelvin, between about 1 Kelvin to about 200 Kelvin, between about 1Kelvin to about 300 Kelvin, between about 1 Kelvin to about10{circumflex over ( )}3 Kelvin, between about 5 Kelvin to about 10Kelvin, between about 5 Kelvin to about 25 Kelvin, between about 5Kelvin to about 50 Kelvin, between about 5 Kelvin to about 100 Kelvin,between about 5 Kelvin to about 200 Kelvin, between about 5 Kelvin toabout 300 Kelvin, between about 5 Kelvin to about 10{circumflex over( )}3 Kelvin, between about 10 Kelvin to about 25 Kelvin, between about10 Kelvin to about 50 Kelvin, between about 10 Kelvin to about 100Kelvin, between about 10 Kelvin to about 200 Kelvin, between about 10Kelvin to about 300 Kelvin, between about 10 Kelvin to about10{circumflex over ( )}3 Kelvin, between about 25 Kelvin to about 50Kelvin, between about 25 Kelvin to about 100 Kelvin, between about 25Kelvin to about 200 Kelvin, between about 25 Kelvin to about 300 Kelvin,between about 25 Kelvin to about 10{circumflex over ( )}3 Kelvin,between about 50 Kelvin to about 100 Kelvin, between about 50 Kelvin toabout 200 Kelvin, between about 50 Kelvin to about 300 Kelvin, betweenabout 50 Kelvin to about 10{circumflex over ( )}3 Kelvin, between about100 Kelvin to about 200 Kelvin, between about 100 Kelvin to about 300Kelvin, between about 100 Kelvin to about 10{circumflex over ( )}3Kelvin, between about 200 Kelvin to about 300 Kelvin, between about 200Kelvin to about 10{circumflex over ( )}3 Kelvin, or between about 300Kelvin to about 10{circumflex over ( )}3 Kelvin. In some embodiments,the cavity comprises a thermal reservoir with a temperature of about10{circumflex over ( )}-3 Kelvin, about 1 Kelvin, about 5 Kelvin, about10 Kelvin, about 25 Kelvin, about 50 Kelvin, about 75 Kelvin, about 100Kelvin, about 150 Kelvin, about 200 Kelvin, about 300 Kelvin, or about10{circumflex over ( )}3 Kelvin, including increments therein.

In some embodiments, the electromagnetic wave comprises a transversemagnetic wave with a polar mode number of N1 and an azimuthal modenumber of N2, where N1 and N2 are an integers from 0 to 1000, and N1 isgreater than or equal to N2. In some embodiments, the electromagneticwave comprises a transverse magnetic wave with a polar mode number of Nand an azimuthal mode number of 0, where N is an integer from 0 to 1000.In some embodiments, the electromagnetic wave comprises a transversemagnetic wave with a polar mode number of N and an azimuthal mode numberof N, where N is an integer from 0 to 1000. In some embodiments, theelectromagnetic wave comprises a transverse electric wave with a polarmode number of N1 and an azimuthal mode number of N2, where N1 and N2are an integers from 0 to 1000, and N1 is greater than or equal to N2.In some embodiments, the electromagnetic wave comprises a transverseelectric wave with a polar mode number of N and an azimuthal mode numberof 0, where N is an integer from 0 to 1000.

In some embodiments, the electromagnetic wave comprises a transverseelectric wave with a polar mode number of N and an azimuthal mode numberof N, where N is an integer from 0 to 1000.

In some embodiments, the electromagnetic radiation source is locatedinside the cavity at, or adjacent to, a maximum field amplitude or anasymptotic field amplitude of the electromagnetic wave.

In some embodiments, the cavity has at least one of a width and a heightbetween about 10{circumflex over ( )}-9 meters to about 10{circumflexover ( )}3 meters. In some embodiments, the cavity has at least one of awidth and a height of at least about 10{circumflex over ( )}-9 meters.In some embodiments, the cavity has at least one of a width and a heightof at most about 10{circumflex over ( )}3 meters. In some embodiments,the cavity has at least one of a width and a height between about10{circumflex over ( )}-9 meters to about 10{circumflex over ( )}-6meters, between about 10{circumflex over ( )}-9 meters to about10{circumflex over ( )}-3 meters, between about 10{circumflex over( )}-9 meters to about 10{circumflex over ( )}-2 meters, between about10{circumflex over ( )}-9 meters to about 10{circumflex over ( )}-1meters, between about 10{circumflex over ( )}-9 meters to about 1.0meter, between about 10{circumflex over ( )}-9 meters to about10{circumflex over ( )}3 meters, between about 10{circumflex over ( )}-6meters to about 10{circumflex over ( )}-3 meters, between about10{circumflex over ( )}-6 meters to about 10{circumflex over ( )}-2meters, between about 10{circumflex over ( )}-6 meters to about10{circumflex over ( )}-1 meters, between about 10{circumflex over( )}-6 meters to about 1.0 meter, between about 10{circumflex over( )}-6 meters to about 10{circumflex over ( )}3 meters, between about10{circumflex over ( )}-3 meters to about 10{circumflex over ( )}-2meters, between about 10{circumflex over ( )}-3 meters to about10{circumflex over ( )}-1 meters, between about 10{circumflex over( )}-3 meters to about 1.0 meter, between about 10{circumflex over( )}-3 meters to about 10{circumflex over ( )}3 meters, between about10{circumflex over ( )}-2 meters to about 10{circumflex over ( )}-1meters, between about 10{circumflex over ( )}-2 meters to about 1.0meter, between about 10{circumflex over ( )}-2 meters to about10{circumflex over ( )}3 meters, between about 10{circumflex over ( )}-1meters to about 1.0 meter, between about 10{circumflex over ( )}-1meters to about 10{circumflex over ( )}3 meters, or between about 1.0meter to about 10{circumflex over ( )}3 meters. In some embodiments, thecavity has at least one of a width and a height of about 10{circumflexover ( )}-9 meters, about 10{circumflex over ( )}-6 meters, about10{circumflex over ( )}-3 meters, about 10{circumflex over ( )}-2meters, about 10{circumflex over ( )}-1 meters, about 1.0 meter, orabout 10{circumflex over ( )}3 meters, including increments therein.

In some embodiments, two or more of the at least three tapered interiorsurfaces form an aperture angle between about 5 degrees to about 175degrees. In some embodiments, two or more of the at least three taperedinterior surfaces form an aperture angle of at least about 5 degrees. Insome embodiments, two or more of the at least three tapered interiorsurfaces form an aperture angle of at most about 175 degrees. In someembodiments, two or more of the at least three tapered interior surfacesform an aperture angle between about 5 degrees to about 10 degrees,between about 5 degrees to about 20 degrees, between about 5 degrees toabout 40 degrees, between about 5 degrees to about 60 degrees, betweenabout 5 degrees to about 80 degrees, between about 5 degrees to about100 degrees, between about 5 degrees to about 120 degrees, between about5 degrees to about 140 degrees, between about 5 degrees to about 160degrees, between about 5 degrees to about 175 degrees, between about 10degrees to about 20 degrees, between about 10 degrees to about 40degrees, between about 10 degrees to about 60 degrees, between about 10degrees to about 80 degrees, between about 10 degrees to about 100degrees, between about 10 degrees to about 120 degrees, between about 10degrees to about 140 degrees, between about 10 degrees to about 160degrees, between about 10 degrees to about 175 degrees, between about 20degrees to about 40 degrees, between about 20 degrees to about 60degrees, between about 20 degrees to about 80 degrees, between about 20degrees to about 100 degrees, between about 20 degrees to about 120degrees, between about 20 degrees to about 140 degrees, between about 20degrees to about 160 degrees, between about 20 degrees to about 175degrees, between about 40 degrees to about 60 degrees, between about 40degrees to about 80 degrees, between about 40 degrees to about 100degrees, between about 40 degrees to about 120 degrees, between about 40degrees to about 140 degrees, between about 40 degrees to about 160degrees, between about 40 degrees to about 175 degrees, between about 60degrees to about 80 degrees, between about 60 degrees to about 100degrees, between about 60 degrees to about 120 degrees, between about 60degrees to about 140 degrees, between about 60 degrees to about 160degrees, between about 60 degrees to about 175 degrees, between about 80degrees to about 100 degrees, between about 80 degrees to about 120degrees, between about 80 degrees to about 140 degrees, between about 80degrees to about 160 degrees, between about 80 degrees to about 175degrees, between about 100 degrees to about 120 degrees, between about100 degrees to about 140 degrees, between about 100 degrees to about 160degrees, between about 100 degrees to about 175 degrees, between about120 degrees to about 140 degrees, between about 120 degrees to about 160degrees, between about 120 degrees to about 175 degrees, between about140 degrees to about 160 degrees, between about 140 degrees to about 175degrees, or between about 160 degrees to about 175 degrees. In someembodiments, two or more of the at least three tapered interior surfacesform an aperture angle of about 5 degrees, about 10 degrees, about 20degrees, about 40 degrees, about 60 degrees, about 80 degrees, about 100degrees, about 120 degrees, about 140 degrees, about 160 degrees, orabout 175 degrees, including increments therein.

In some embodiments, the cavity has a wall with a wall thickness betweenabout 10{circumflex over ( )}-9 meters to about 1.0 meter. In someembodiments, the cavity has a wall with a wall thickness of at leastabout 10{circumflex over ( )}-9 meters. In some embodiments, the cavityhas a wall with a wall thickness of at most about 1.0 meter. In someembodiments, the cavity has a wall with a wall thickness between about10{circumflex over ( )}-9 meters to about 10{circumflex over ( )}-6meters, between about 10{circumflex over ( )}-9 meters to about10{circumflex over ( )}-5 meters, between about 10{circumflex over( )}-9 meters to about 10{circumflex over ( )}-4 meters, between about10{circumflex over ( )}-9 meters to about 10{circumflex over ( )}-3meters, between about 10{circumflex over ( )}-9 meters to about 1.0meter, between about 10{circumflex over ( )}-6 meters to about10{circumflex over ( )}-5 meters, between about 10{circumflex over( )}-6 meters to about 10{circumflex over ( )}-4 meters, between about10{circumflex over ( )}-6 meters to about 10{circumflex over ( )}-3meters, between about 10{circumflex over ( )}-6 meters to about 1.0meter, between about 10{circumflex over ( )}-5 meters to about10{circumflex over ( )}-4 meters, between about 10{circumflex over( )}-5 meters to about 10{circumflex over ( )}-3 meters, between about10{circumflex over ( )}-5 meters to about 1.0 meter, between about10{circumflex over ( )}-4 meters to about 10{circumflex over ( )}-3meters, between about 10{circumflex over ( )}-4 meters to about 1.0meter, or between about 10{circumflex over ( )}-3 meters to about 1.0meter. In some embodiments, the cavity has a wall with a wall thicknessof about 10{circumflex over ( )}-9 meters, about 10{circumflex over( )}-6 meters, about 10{circumflex over ( )}-5 meters, about10{circumflex over ( )}-4 meters, about 10{circumflex over ( )}-3meters, or about 1.0 meter, including increments therein.

In some embodiments, the base interior surface of the cavity comprises3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22,23, or 24 sides. In some embodiments, the base interior surface of thecavity is substantially equilateral. In some embodiments, the baseinterior surface is substantially flat.

In some embodiments, the electromagnetic wave forms an electromagneticenergy momentum tensor with an amplitude maximum at, or adjacent to, thebase interior surface, which results in one or more of a metric tensorcurvature, a thrust, and an acceleration of the thruster. In someembodiments, the electromagnetic wave forms an electromagnetic energymomentum tensor with an amplitude maximum at, or adjacent to, one ormore of the at least three tapered interior surfaces and the apex point,which results in one or more of a metric tensor curvature, a thrust, andan acceleration of the thruster.

Another embodiment includes an electromagnetic energy momentum thrustercomprising: a cavity resonator forming a pyramidal cavity having a baseinterior surface, at least three tapered interior surfaces, and atruncated interior surface opposing the base interior surface, thetapered interior surfaces being between the base and truncated interiorsurfaces; and an electromagnetic radiation source in communication withthe cavity resonator, the electromagnetic radiation source configured toemit an electromagnetic wave having a frequency between about 1.0 MHz toabout 1000 THz into the cavity resonator.

In some embodiments, the electromagnetic radiation source is configuredto emit an electromagnetic wave into the cavity resonator having afrequency between about 10{circumflex over ( )}0 MHz to about10{circumflex over ( )}9 MHz. In some embodiments, the electromagneticradiation source is configured to emit an electromagnetic wave into thecavity resonator having a frequency of at least about 10{circumflex over( )}0 MHz. In some embodiments, the electromagnetic radiation source isconfigured to emit an electromagnetic wave into the cavity resonatorhaving a frequency of at most about 10{circumflex over ( )}9 MHz. Insome embodiments, the electromagnetic radiation source is configured toemit an electromagnetic wave into the cavity resonator having afrequency between about 10{circumflex over ( )}0 MHz to about10{circumflex over ( )}1 MHz, between about 10{circumflex over ( )}0 MHzto about 10{circumflex over ( )}2 MHz, between about 10{circumflex over( )}0 MHz to about 10{circumflex over ( )}3 MHz, between about10{circumflex over ( )}0 MHz to about 10{circumflex over ( )}4 MHz,between about 10{circumflex over ( )}0 MHz to about 10{circumflex over( )}5 MHz, between about 10{circumflex over ( )}0 MHz to about10{circumflex over ( )}6 MHz, between about 10{circumflex over ( )}0 MHzto about 10{circumflex over ( )}7 MHz, between about 10{circumflex over( )}0 MHz to about 10{circumflex over ( )}8 MHz, between about10{circumflex over ( )}0 MHz to about 10{circumflex over ( )}9 MHz,between about 10{circumflex over ( )}1 MHz to about 10{circumflex over( )}2 MHz, between about 10{circumflex over ( )}1 MHz to about10{circumflex over ( )}3 MHz, between about 10{circumflex over ( )}1 MHzto about 10{circumflex over ( )}4 MHz, between about 10{circumflex over( )}1 MHz to about 10{circumflex over ( )}5 MHz, between about10{circumflex over ( )}1 MHz to about 10{circumflex over ( )}6 MHz,between about 10{circumflex over ( )}1 MHz to about 10{circumflex over( )}7 MHz, between about 10{circumflex over ( )}1 MHz to about10{circumflex over ( )}8 MHz, between about 10{circumflex over ( )}1 MHzto about 10{circumflex over ( )}9 MHz, between about 10{circumflex over( )}2 MHz to about 10{circumflex over ( )}3 MHz, between about10{circumflex over ( )}2 MHz to about 10{circumflex over ( )}4 MHz,between about 10{circumflex over ( )}2 MHz to about 10{circumflex over( )}5 MHz, between about 10{circumflex over ( )}2 MHz to about10{circumflex over ( )}6 MHz, between about 10{circumflex over ( )}2 MHzto about 10{circumflex over ( )}7 MHz, between about 10{circumflex over( )}2 MHz to about 10{circumflex over ( )}8 MHz, between about10{circumflex over ( )}2 MHz to about 10{circumflex over ( )}9 MHz,between about 10{circumflex over ( )}3 MHz to about 10{circumflex over( )}4 MHz, between about 10{circumflex over ( )}3 MHz to about10{circumflex over ( )}5 MHz, between about 10{circumflex over ( )}3 MHzto about 10{circumflex over ( )}6 MHz, between about 10{circumflex over( )}3 MHz to about 10{circumflex over ( )}7 MHz, between about10{circumflex over ( )}3 MHz to about 10{circumflex over ( )}8 MHz,between about 10{circumflex over ( )}3 MHz to about 10{circumflex over( )}9 MHz, between about 10{circumflex over ( )}4 MHz to about10{circumflex over ( )}5 MHz, between about 10{circumflex over ( )}4 MHzto about 10{circumflex over ( )}6 MHz, between about 10{circumflex over( )}4 MHz to about 10{circumflex over ( )}7 MHz, between about10{circumflex over ( )}4 MHz to about 10{circumflex over ( )}8 MHz,between about 10{circumflex over ( )}4 MHz to about 10{circumflex over( )}9 MHz, between about 10{circumflex over ( )}5 MHz to about10{circumflex over ( )}6 MHz, between about 10{circumflex over ( )}5 MHzto about 10{circumflex over ( )}7 MHz, between about 10{circumflex over( )}5 MHz to about 10{circumflex over ( )}8 MHz, between about10{circumflex over ( )}5 MHz to about 10{circumflex over ( )}9 MHz,between about 10{circumflex over ( )}6 MHz to about 10{circumflex over( )}7 MHz, between about 10{circumflex over ( )}6 MHz to about10{circumflex over ( )}8 MHz, between about 10{circumflex over ( )}6 MHzto about 10{circumflex over ( )}9 MHz, between about 10{circumflex over( )}7 MHz to about 10{circumflex over ( )}8 MHz, between about10{circumflex over ( )}7 MHz to about 10{circumflex over ( )}9 MHz, orbetween about 10{circumflex over ( )}8 MHz to about 10{circumflex over( )}9 MHz. In some embodiments, the electromagnetic radiation source isconfigured to emit an electromagnetic wave into the cavity resonatorhaving a frequency of about 10{circumflex over ( )}0 MHz, about10{circumflex over ( )}1 MHz, about 10{circumflex over ( )}2 MHz, about10{circumflex over ( )}3 MHz, about 10{circumflex over ( )}4 MHz, about10{circumflex over ( )}5 MHz, about 10{circumflex over ( )}6 MHz, about10{circumflex over ( )}7 MHz, about 10{circumflex over ( )}8 MHz, orabout 10{circumflex over ( )}9 MHz, including increments therein.

In some embodiments, the electromagnetic radiation source is configuredto produce the frequency of the electromagnetic wave in evanescence sothat the electromagnetic wave has a maximum field amplitude and anasymptotic field amplitude, the maximum field amplitude being at, oradjacent to, the base interior surface, the asymptotic field amplitudebeing at, or adjacent to, one or more of the at least three taperedinterior surfaces and the truncated interior surface. In someembodiments, the electromagnetic radiation source is configured toproduce the frequency of the electromagnetic wave in evanescence so thatthe electromagnetic wave has a maximum field amplitude and an asymptoticfield amplitude, the maximum field amplitude being at, or adjacent to,one or more of the at least three tapered interior surfaces and thetruncated interior surface, the asymptotic field amplitude being at, oradjacent to, the base interior surface.

In some embodiments, the cavity includes an overall interior surfacethat includes the base, tapered, and truncated interior surfaces,substantially the entire overall interior surface being electricallyconductive, wherein the cavity resonator has a quality factor betweenabout 10{circumflex over ( )}3 to about 10{circumflex over ( )}9. Insome embodiments, the cavity resonator has a quality factor of at leastabout 10{circumflex over ( )}3. In some embodiments, the cavityresonator has a quality factor of at most about 10{circumflex over( )}9. In some embodiments, the cavity resonator has a quality factorbetween about 10{circumflex over ( )}3 to about 10{circumflex over( )}4, between about 10{circumflex over ( )}3 to about 10{circumflexover ( )}5, between about 10{circumflex over ( )}3 to about10{circumflex over ( )}6, between about 10{circumflex over ( )}3 toabout 10{circumflex over ( )}7, between about 10{circumflex over ( )}3to about 10{circumflex over ( )}8, between about 10{circumflex over( )}3 to about 10{circumflex over ( )}9, between about 10{circumflexover ( )}4 to about 10{circumflex over ( )}5, about 10{circumflex over( )}4 to about 10{circumflex over ( )}6, about 10{circumflex over ( )}4to about 10{circumflex over ( )}7, about 10{circumflex over ( )}4 toabout 10{circumflex over ( )}8, about 10{circumflex over ( )}4 to about10{circumflex over ( )}9, about 10{circumflex over ( )}5 to about10{circumflex over ( )}6, about 10{circumflex over ( )}5 to about10{circumflex over ( )}7, about 10{circumflex over ( )}5 to about10{circumflex over ( )}8, about 10{circumflex over ( )}5 to about10{circumflex over ( )}9, about 10{circumflex over ( )}6 to about10{circumflex over ( )}7, about 10{circumflex over ( )}6 to about10{circumflex over ( )}8, about 10{circumflex over ( )}6 to about10{circumflex over ( )}9, about 10{circumflex over ( )}7 to about10{circumflex over ( )}8, about 10{circumflex over ( )}7 to about10{circumflex over ( )}9, or about 10{circumflex over ( )}8 to about10{circumflex over ( )}9. In some embodiments, the cavity resonator hasa quality factor of about 10{circumflex over ( )}3, about 10{circumflexover ( )}4, about 10{circumflex over ( )}5, about 10{circumflex over( )}6, about 10{circumflex over ( )}7, about 10{circumflex over ( )}8,or about 10{circumflex over ( )}9, including increments therein.

In some embodiments, the overall interior surface comprises aluminum,antimony, arsenic, barium, beryllium, bismuth, cadmium, calcium, carbon,chromium, cobalt, copper, gallium, gold, hydrogen, indium, iron,lanthanum, lead, lithium, magnesium, manganese, mercury, molybdenum,nickel, niobium, nitrogen, oxygen, palladium, phosphorus, platinum,scandium, silicon, silver, strontium, sulfur, tantalum, technetium, tin,titanium, tungsten, vanadium, yttrium, zinc, zirconium, or anycombination thereof.

In some embodiments, the cavity includes an overall interior surfacethat includes the base, tapered, and truncated interior surfaces,substantially the entire overall interior surface being superconductive,wherein the cavity resonator has a quality factor between about10{circumflex over ( )}6 to about 10{circumflex over ( )}15. In someembodiments, the cavity resonator has a quality factor of at least about10{circumflex over ( )}6. In some embodiments, the cavity resonator hasa quality factor of at most about 10{circumflex over ( )}15. In someembodiments, the cavity resonator has a quality factor between about10{circumflex over ( )}6 to about 10{circumflex over ( )}7, betweenabout 10{circumflex over ( )}6 to about 10{circumflex over ( )}8,between about 10{circumflex over ( )}6 to about 10{circumflex over( )}9, between about 10{circumflex over ( )}6 to about 10{circumflexover ( )}10, between about 10{circumflex over ( )}6 to about10{circumflex over ( )}11, between about 10{circumflex over ( )}6 toabout 10{circumflex over ( )}12, between about 10{circumflex over ( )}6to about 10{circumflex over ( )}13, between about 10{circumflex over( )}6 to about 10{circumflex over ( )}14, between about 10{circumflexover ( )}6 to about 10{circumflex over ( )}15, between about10{circumflex over ( )}7 to about 10{circumflex over ( )}8, betweenabout 10{circumflex over ( )}7 to about 10{circumflex over ( )}9,between about 10{circumflex over ( )}7 to about 10{circumflex over( )}10, between about 10{circumflex over ( )}7 to about 10{circumflexover ( )}11, between about 10{circumflex over ( )}7 to about10{circumflex over ( )}12, between about 10{circumflex over ( )}7 toabout 10{circumflex over ( )}13, between about 10{circumflex over ( )}7to about 10{circumflex over ( )}14, between about 10{circumflex over( )}7 to about 10{circumflex over ( )}15, between about 10{circumflexover ( )}8 to about 10{circumflex over ( )}9, between about10{circumflex over ( )}8 to about 10{circumflex over ( )}10, betweenabout 10{circumflex over ( )}8 to about 10{circumflex over ( )}11,between about 10{circumflex over ( )}8 to about 10{circumflex over( )}12, between about 10{circumflex over ( )}8 to about 10{circumflexover ( )}13, between about 10{circumflex over ( )}8 to about10{circumflex over ( )}14, between about 10{circumflex over ( )}8 toabout 10{circumflex over ( )}15, between about 10{circumflex over ( )}9to about 10{circumflex over ( )}10, between about 10{circumflex over( )}9 to about 10{circumflex over ( )}11, between about 10{circumflexover ( )}9 to about 10{circumflex over ( )}12, between about10{circumflex over ( )}9 to about 10{circumflex over ( )}13, betweenabout 10{circumflex over ( )}9 to about 10{circumflex over ( )}14,between about 10{circumflex over ( )}9 to about 10{circumflex over( )}15, between about 10{circumflex over ( )}10 to about 10{circumflexover ( )}11, between about 10{circumflex over ( )}10 to about10{circumflex over ( )}12, between about 10{circumflex over ( )}10 toabout 10{circumflex over ( )}13, between about 10{circumflex over ( )}10to about 10{circumflex over ( )}14, between about 10{circumflex over( )}10 to about 10{circumflex over ( )}15, between about 10{circumflexover ( )}11 to about 10{circumflex over ( )}12, between about10{circumflex over ( )}11 to about 10{circumflex over ( )}13, betweenabout 10{circumflex over ( )}11 to about 10{circumflex over ( )}14,between about 10{circumflex over ( )}11 to about 10{circumflex over( )}15, between about 10{circumflex over ( )}12 to about 10{circumflexover ( )}13, between about 10{circumflex over ( )}12 to about10{circumflex over ( )}14, between about 10{circumflex over ( )}12 toabout 10{circumflex over ( )}15, between about 10{circumflex over ( )}13to about 10{circumflex over ( )}14, between about 10{circumflex over( )}13 to about 10{circumflex over ( )}15, or between about10{circumflex over ( )}14 to about 10{circumflex over ( )}15. In someembodiments, the cavity resonator has a quality factor of about10{circumflex over ( )}6, about 10{circumflex over ( )}7, about10{circumflex over ( )}8, about 10{circumflex over ( )}9, about10{circumflex over ( )}10, about 10{circumflex over ( )}11, about10{circumflex over ( )}12, about 10{circumflex over ( )}13, about10{circumflex over ( )}14, or about 10{circumflex over ( )}15, includingincrements therein.

In some embodiments, the overall interior surface comprises aluminum,barium, beryllium, bismuth, cadmium, calcium, copper, gallium,gadolinium, germanium, lanthanum, lead, lithium, indium, mercury,molybdenum, niobium, nitrogen, osmium, oxygen, protactinium, rhenium,ruthenium, silicon, strontium, sulfur, tantalum, technetium, thallium,thorium, titanium, tin, vanadium, yttrium, zinc, zirconium, NbTi, PbMoS,V₃Ga, NbN, V₃Si, Nb₃Sn, Nb₃Al, Nb₃(AlGe), Nb₃Ge, Bi₂Sr₂CuO₆,Bi₂Sr₂CaCu₂O₈, Bi₂Sr₂Ca₂Cu₃O₁₀, YBa₂Cu₃O₇, YBa₂Cu₄O₈, Y₂Ba₄Cu₇O₁₅,Y₃Ba₅Cu₈O₁₈, Tl₂Ba₂CuO₆, Tl₂Ba₂CaCu₂O₈, Tl₂Ba₂Ca₂Cu₃O₁₀, TlBa₂Ca₃Cu₄O₁₁,HgBa₂CuO₄, HgBa₂CaCu₂O₆, HgBa₂Ca₂Cu₃O₈, or any combination thereof.

In some embodiments, the cavity is empty. In some embodiments, thecavity comprises a vacuum with a pressure between about 10{circumflexover ( )}-24 Torr to about 10{circumflex over ( )}3 Torr. In someembodiments, the cavity comprises a vacuum with a pressure of at leastabout 10{circumflex over ( )}-24 Torr. In some embodiments, the cavitycomprises a vacuum with a pressure of at most about 10{circumflex over( )}3 Torr. In some embodiments, the cavity comprises a vacuum with apressure between about 10{circumflex over ( )}-24 Torr to about10{circumflex over ( )}-21 Torr, between about 10{circumflex over( )}-24 Torr to about 10{circumflex over ( )}-18 Torr, between about10{circumflex over ( )}-24 Torr to about 10{circumflex over ( )}-15Torr, between about 10{circumflex over ( )}-24 Torr to about10{circumflex over ( )}-12 Torr, between about 10{circumflex over( )}-24 Torr to about 10{circumflex over ( )}-9 Torr, between about10{circumflex over ( )}-24 Torr to about 10{circumflex over ( )}-6 Torr,between about 10{circumflex over ( )}-24 Torr to about 10{circumflexover ( )}-3 Torr, between about 10{circumflex over ( )}-24 Torr to about1.0 Torr, between about 10{circumflex over ( )}-24 Torr to about10{circumflex over ( )}3 Torr, between about 10{circumflex over ( )}-21Torr to about 10{circumflex over ( )}-18 Torr, between about10{circumflex over ( )}-21 Torr to about 10{circumflex over ( )}-15Torr, between about 10{circumflex over ( )}-21 Torr to about10{circumflex over ( )}-12 Torr, between about 10{circumflex over( )}-21 Torr to about 10{circumflex over ( )}-9 Torr, between about10{circumflex over ( )}-21 Torr to about 10{circumflex over ( )}-6 Torr,between about 10{circumflex over ( )}-21 Torr to about 10{circumflexover ( )}-3 Torr, between about 10{circumflex over ( )}-21 Torr to about1.0 Torr, between about 10{circumflex over ( )}-21 Torr to about10{circumflex over ( )}3 Torr, between about 10{circumflex over ( )}-18Torr to about 10{circumflex over ( )}-15 Torr, between about10{circumflex over ( )}-18 Torr to about 10{circumflex over ( )}-12Torr, between about 10{circumflex over ( )}-18 Torr to about10{circumflex over ( )}-9 Torr, between about 10{circumflex over ( )}-18Torr to about 10{circumflex over ( )}-6 Torr, between about10{circumflex over ( )}-18 Torr to about 10{circumflex over ( )}-3 Torr,between about 10{circumflex over ( )}-18 Torr to about 1.0 Torr, betweenabout 10{circumflex over ( )}-18 Torr to about 10{circumflex over ( )}3Torr, between about 10{circumflex over ( )}-15 Torr to about10{circumflex over ( )}-12 Torr, between about 10{circumflex over( )}-15 Torr to about 10{circumflex over ( )}-9 Torr, between about10{circumflex over ( )}-15 Torr to about 10{circumflex over ( )}-6 Torr,between about 10{circumflex over ( )}-15 Torr to about 10{circumflexover ( )}-3 Torr, between about 10{circumflex over ( )}-15 Torr to about1.0 Torr, between about 10{circumflex over ( )}-15 Torr to about10{circumflex over ( )}3 Torr, between about 10{circumflex over ( )}-12Torr to about 10{circumflex over ( )}-9 Torr, between about10{circumflex over ( )}-12 Torr to about 10{circumflex over ( )}-6 Torr,between about 10{circumflex over ( )}-12 Torr to about 10{circumflexover ( )}-3 Torr, between about 10{circumflex over ( )}-12 Torr to about1.0 Torr, between about 10{circumflex over ( )}-12 Torr to about10{circumflex over ( )}3 Torr, between about 10{circumflex over ( )}-9Torr to about 10{circumflex over ( )}-6 Torr, between about10{circumflex over ( )}-9 Torr to about 10{circumflex over ( )}-3 Torr,between about 10{circumflex over ( )}-9 Torr to about 1.0 Torr, betweenabout 10{circumflex over ( )}-9 Torr to about 10{circumflex over ( )}3Torr, between about 10{circumflex over ( )}-6 Torr to about10{circumflex over ( )}-3 Torr, between about 10{circumflex over ( )}-6Torr to about 1.0 Torr, between about 10{circumflex over ( )}-6 Torr toabout 10{circumflex over ( )}3 Torr, between about 10{circumflex over( )}-3 Torr to about 1.0 Torr, between about 10{circumflex over ( )}-3Torr to about 10{circumflex over ( )}3 Torr, or between about 1.0 Torrto about 10{circumflex over ( )}3 Torr. In some embodiments, the cavitycomprises a vacuum with a pressure of about 10{circumflex over ( )}-24Torr, about 10{circumflex over ( )}-21 Torr, about 10{circumflex over( )}-18 Torr, about 10{circumflex over ( )}-15 Torr, about 10{circumflexover ( )}-12 Torr, about 10{circumflex over ( )}-9 Torr, about10{circumflex over ( )}-6 Torr, about 10{circumflex over ( )}-3 Torr,about 1.0 Torr, or about 10{circumflex over ( )}3 Torr, includingincrements therein.

In some embodiments, the cavity comprises a thermal reservoir with atemperature between about 10{circumflex over ( )}-3 Kelvin about10{circumflex over ( )}3 Kelvin. In some embodiments, the cavitycomprises a thermal reservoir with a temperature of at least about10{circumflex over ( )}-3 Kelvin. In some embodiments, the cavitycomprises a thermal reservoir with a temperature of at most about10{circumflex over ( )}3 Kelvin. In some embodiments, the cavitycomprises a thermal reservoir with a temperature between about10{circumflex over ( )}-3 Kelvin to about 1 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 5 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 10 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 25 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 50 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 100 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 200 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 300 Kelvin, between about10{circumflex over ( )}-3 Kelvin to about 10{circumflex over ( )}3Kelvin, between about 1 Kelvin to about 5 Kelvin, between about 1 Kelvinto about 10 Kelvin, between about 1 Kelvin to about 25 Kelvin, betweenabout 1 Kelvin to about 50 Kelvin, between about 1 Kelvin to about 100Kelvin, between about 1 Kelvin to about 200 Kelvin, between about 1Kelvin to about 300 Kelvin, between about 1 Kelvin to about10{circumflex over ( )}3 Kelvin, between about 5 Kelvin to about 10Kelvin, between about 5 Kelvin to about 25 Kelvin, between about 5Kelvin to about 50 Kelvin, between about 5 Kelvin to about 100 Kelvin,between about 5 Kelvin to about 200 Kelvin, between about 5 Kelvin toabout 300 Kelvin, between about 5 Kelvin to about 10{circumflex over( )}3 Kelvin, between about 10 Kelvin to about 25 Kelvin, between about10 Kelvin to about 50 Kelvin, between about 10 Kelvin to about 100Kelvin, between about 10 Kelvin to about 200 Kelvin, between about 10Kelvin to about 300 Kelvin, between about 10 Kelvin to about10{circumflex over ( )}3 Kelvin, between about 25 Kelvin to about 50Kelvin, between about 25 Kelvin to about 100 Kelvin, between about 25Kelvin to about 200 Kelvin, between about 25 Kelvin to about 300 Kelvin,between about 25 Kelvin to about 10{circumflex over ( )}3 Kelvin,between about 50 Kelvin to about 100 Kelvin, between about 50 Kelvin toabout 200 Kelvin, between about 50 Kelvin to about 300 Kelvin, betweenabout 50 Kelvin to about 10{circumflex over ( )}3 Kelvin, between about100 Kelvin to about 200 Kelvin, between about 100 Kelvin to about 300Kelvin, between about 100 Kelvin to about 10{circumflex over ( )}3Kelvin, between about 200 Kelvin to about 300 Kelvin, between about 200Kelvin to about 10{circumflex over ( )}3 Kelvin, or between about 300Kelvin to about 10{circumflex over ( )}3 Kelvin. In some embodiments,the cavity comprises a thermal reservoir with a temperature of about10{circumflex over ( )}-3 Kelvin, about 1 Kelvin, about 5 Kelvin, about10 Kelvin, about 25 Kelvin, about 50 Kelvin, about 75 Kelvin, about 100Kelvin, about 150 Kelvin, about 200 Kelvin, about 300 Kelvin, or about10{circumflex over ( )}3 Kelvin, including increments therein.

In some embodiments, the electromagnetic wave comprises a transversemagnetic wave with a polar mode number of N1 and an azimuthal modenumber of N2, where N1 and N2 are an integers from 0 to 1000, and N1 isgreater than or equal to N2. In some embodiments, the electromagneticwave comprises a transverse magnetic wave with a polar mode number of Nand an azimuthal mode number of 0, where N is an integer from 0 to 1000.In some embodiments, the electromagnetic wave comprises a transversemagnetic wave with a polar mode number of N and an azimuthal mode numberof N, where N is an integer from 0 to 1000. In some embodiments, theelectromagnetic wave comprises a transverse electric wave with a polarmode number of N1 and an azimuthal mode number of N2, where N1 and N2are an integers from 0 to 1000, and N1 is greater than or equal to N2.In some embodiments, the electromagnetic wave comprises a transverseelectric wave with a polar mode number of N and an azimuthal mode numberof 0, where N is an integer from 0 to 1000. In some embodiments, theelectromagnetic wave comprises a transverse electric wave with a polarmode number of N and an azimuthal mode number of N, where N is aninteger from 0 to 1000.

In some embodiments, the electromagnetic radiation source is locatedinside the cavity at, or adjacent to, a maximum field amplitude or anasymptotic field amplitude of the electromagnetic wave.

In some embodiments, the cavity has at least one of a width and a heightbetween about 10{circumflex over ( )}-9 meters to about 10{circumflexover ( )}3 meters. In some embodiments, the cavity has at least one of awidth and a height of at least about 10{circumflex over ( )}-9 meters.In some embodiments, the cavity has at least one of a width and a heightof at most about 10{circumflex over ( )}3 meters. In some embodiments,the cavity has at least one of a width and a height between about10{circumflex over ( )}-9 meters to about 10{circumflex over ( )}-6meters, between about 10{circumflex over ( )}-9 meters to about10{circumflex over ( )}-3 meters, between about 10{circumflex over( )}-9 meters to about 10{circumflex over ( )}-2 meters, between about10{circumflex over ( )}-9 meters to about 10{circumflex over ( )}-1meters, between about 10{circumflex over ( )}-9 meters to about 1.0meter, between about 10{circumflex over ( )}-9 meters to about10{circumflex over ( )}3 meters, between about 10{circumflex over ( )}-6meters to about 10{circumflex over ( )}-3 meters, between about10{circumflex over ( )}-6 meters to about 10{circumflex over ( )}-2meters, between about 10{circumflex over ( )}-6 meters to about10{circumflex over ( )}-1 meters, between about 10{circumflex over( )}-6 meters to about 1.0 meter, between about 10{circumflex over( )}-6 meters to about 10{circumflex over ( )}3 meters, between about10{circumflex over ( )}-3 meters to about 10{circumflex over ( )}-2meters, between about 10{circumflex over ( )}-3 meters to about10{circumflex over ( )}-1 meters, between about 10{circumflex over( )}-3 meters to about 1.0 meter, between about 10{circumflex over( )}-3 meters to about 10{circumflex over ( )}3 meters, between about10{circumflex over ( )}-2 meters to about 10{circumflex over ( )}-1meters, between about 10{circumflex over ( )}-2 meters to about 1.0meter, between about 10{circumflex over ( )}-2 meters to about10{circumflex over ( )}3 meters, between about 10{circumflex over ( )}-1meters to about 1.0 meter, between about 10{circumflex over ( )}-1meters to about 10{circumflex over ( )}3 meters, or between about 1.0meter to about 10{circumflex over ( )}3 meters. In some embodiments, thecavity has at least one of a width and a height of about 10{circumflexover ( )}-9 meters, about 10{circumflex over ( )}-6 meters, about10{circumflex over ( )}-3 meters, about 10{circumflex over ( )}-2meters, about 10{circumflex over ( )}-1 meters, about 1.0 meter, orabout 10{circumflex over ( )}3 meters, including increments therein.

In some embodiments, two or more of the at least three tapered interiorsurfaces form an aperture angle between about 5 degrees to about 175degrees. In some embodiments, two or more of the at least three taperedinterior surfaces form an aperture angle of at least about 5 degrees. Insome embodiments, two or more of the at least three tapered interiorsurfaces form an aperture angle of at most about 175 degrees. In someembodiments, two or more of the at least three tapered interior surfacesform an aperture angle between about 5 degrees to about 10 degrees,between about 5 degrees to about 20 degrees, between about 5 degrees toabout 40 degrees, between about 5 degrees to about 60 degrees, betweenabout 5 degrees to about 80 degrees, between about 5 degrees to about100 degrees, between about 5 degrees to about 120 degrees, between about5 degrees to about 140 degrees, between about 5 degrees to about 160degrees, between about 5 degrees to about 175 degrees, between about 10degrees to about 20 degrees, between about 10 degrees to about 40degrees, between about 10 degrees to about 60 degrees, between about 10degrees to about 80 degrees, between about 10 degrees to about 100degrees, between about 10 degrees to about 120 degrees, between about 10degrees to about 140 degrees, between about 10 degrees to about 160degrees, between about 10 degrees to about 175 degrees, between about 20degrees to about 40 degrees, between about 20 degrees to about 60degrees, between about 20 degrees to about 80 degrees, between about 20degrees to about 100 degrees, between about 20 degrees to about 120degrees, between about 20 degrees to about 140 degrees, between about 20degrees to about 160 degrees, between about 20 degrees to about 175degrees, between about 40 degrees to about 60 degrees, between about 40degrees to about 80 degrees, between about 40 degrees to about 100degrees, between about 40 degrees to about 120 degrees, between about 40degrees to about 140 degrees, between about 40 degrees to about 160degrees, between about 40 degrees to about 175 degrees, between about 60degrees to about 80 degrees, between about 60 degrees to about 100degrees, between about 60 degrees to about 120 degrees, between about 60degrees to about 140 degrees, between about 60 degrees to about 160degrees, between about 60 degrees to about 175 degrees, between about 80degrees to about 100 degrees, between about 80 degrees to about 120degrees, between about 80 degrees to about 140 degrees, between about 80degrees to about 160 degrees, between about 80 degrees to about 175degrees, between about 100 degrees to about 120 degrees, between about100 degrees to about 140 degrees, between about 100 degrees to about 160degrees, between about 100 degrees to about 175 degrees, between about120 degrees to about 140 degrees, between about 120 degrees to about 160degrees, between about 120 degrees to about 175 degrees, between about140 degrees to about 160 degrees, between about 140 degrees to about 175degrees, or between about 160 degrees to about 175 degrees. In someembodiments, two or more of the at least three tapered interior surfacesform an aperture angle of about 5 degrees, about 10 degrees, about 20degrees, about 40 degrees, about 60 degrees, about 80 degrees, about 100degrees, about 120 degrees, about 140 degrees, about 160 degrees, orabout 175 degrees, including increments therein.

In some embodiments, the cavity has a wall with a wall thickness betweenabout 10{circumflex over ( )}-9 meters to about 1.0 meter. In someembodiments, the cavity has a wall with a wall thickness of at leastabout 10{circumflex over ( )}-9 meters. In some embodiments, the cavityhas a wall with a wall thickness of at most about 1.0 meter. In someembodiments, the cavity has a wall with a wall thickness between about10{circumflex over ( )}-9 meters to about 10{circumflex over ( )}-6meters, between about 10{circumflex over ( )}-9 meters to about10{circumflex over ( )}-5 meters, between about 10{circumflex over( )}-9 meters to about 10{circumflex over ( )}-4 meters, between about10{circumflex over ( )}-9 meters to about 10{circumflex over ( )}-3meters, between about 10{circumflex over ( )}-9 meters to about 1.0meter, between about 10{circumflex over ( )}-6 meters to about10{circumflex over ( )}-5 meters, between about 10{circumflex over( )}-6 meters to about 10{circumflex over ( )}-4 meters, between about10{circumflex over ( )}-6 meters to about 10{circumflex over ( )}-3meters, between about 10{circumflex over ( )}-6 meters to about 1.0meter, between about 10{circumflex over ( )}-5 meters to about10{circumflex over ( )}-4 meters, between about 10{circumflex over( )}-5 meters to about 10{circumflex over ( )}-3 meters, between about10{circumflex over ( )}-5 meters to about 1.0 meter, between about10{circumflex over ( )}-4 meters to about 10{circumflex over ( )}-3meters, between about 10{circumflex over ( )}-4 meters to about 1.0meter, or between about 10{circumflex over ( )}-3 meters to about 1.0meter. In some embodiments, the cavity has a wall with a wall thicknessof about 10{circumflex over ( )}-9 meters, about 10{circumflex over( )}-6 meters, about 10{circumflex over ( )}-5 meters, about10{circumflex over ( )}-4 meters, about 10{circumflex over ( )}-3meters, or about 1.0 meter, including increments therein.

In some embodiments, one or both the base interior surface and thetruncated interior surface of the cavity comprises 3, 4, 5, 6, 7, 8, 9,10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, or 24 sides. Insome embodiments, one or both the base interior surface and thetruncated interior surface of the cavity is substantially equilateral.In some embodiments, one or both the base interior surface and thetruncated interior surface of the cavity is substantially flat.

In some embodiments, the electromagnetic wave forms an electromagneticenergy momentum tensor with an amplitude maximum at, or adjacent to, thebase interior surface, which results in one or more of a metric tensorcurvature, a thrust, and an acceleration of the thruster. In someembodiments, the electromagnetic wave forms an electromagnetic energymomentum tensor with an amplitude maximum at, or adjacent to, one ormore of the at least three tapered interior surfaces and the truncatedinterior surface, which results in one or more of a metric tensorcurvature, a thrust, and an acceleration of the thruster.

BRIEF DESCRIPTION OF THE DRAWINGS

Various novel features of the disclosure are set forth withparticularity in the appended claims. A better understanding of thefeatures and advantages of the present disclosure will be obtained byreference to the following detailed description that sets forthillustrative embodiments and the accompanying drawings.

FIG. 1 is an exemplary schematic diagram of a non-limitingelectromagnetic energy momentum thruster.

FIG. 2 is an exemplary perspective view of a non-limiting conical cavityresonator.

FIG. 3 is an exemplary perspective cross section view of a non-limitingconical cavity resonator.

FIG. 4 is an exemplary perspective view of a non-limiting truncatedconical cavity resonator.

FIG. 5 is an exemplary perspective cross section view of a non-limitingtruncated conical cavity resonator.

FIG. 6 is an exemplary perspective view of a non-limiting pyramidalcavity resonator.

FIG. 7 is an exemplary perspective cross section view of a non-limitingpyramidal cavity resonator.

FIG. 8 is an exemplary perspective view of a non-limiting truncatedpyramidal cavity resonator.

FIG. 9 is an exemplary perspective cross section view of a non-limitingtruncated pyramidal cavity resonator.

FIG. 10 is an exemplary cross section view of a non-limiting taperedcavity resonator.

FIG. 11 is an exemplary cross section view of a non-limiting taperedcavity resonator comprising a substantially flat base interior surface.

FIG. 12 is an exemplary cross section view of a non-limiting taperedcavity resonator comprising a base radiation source.

FIG. 13 is an exemplary cross section view of a non-limiting taperedcavity resonator comprising a substantially flat base interior surfaceand a base radiation source.

FIG. 14 is an exemplary cross section view of a non-limiting taperedcavity resonator comprising a side radiation source.

FIG. 15 is an exemplary cross section view of a non-limiting taperedcavity comprising a substantially flat base interior surface and a sideradiation source.

FIG. 16 is an exemplary cross section view of a non-limiting truncatedtapered cavity resonator.

FIG. 17 is an exemplary cross section view of a non-limiting truncatedtapered cavity resonator comprising a substantially flat base andtruncated interior surfaces.

FIG. 18 is an exemplary cross section view of a non-limiting truncatedtapered cavity resonator comprising a base radiation source.

FIG. 19 is an exemplary cross section view of a non-limiting truncatedtapered cavity resonator comprising a substantially flat base andtruncated interior surfaces, and a base radiation source.

FIG. 20 is an exemplary cross section view of a non-limiting truncatedtapered cavity resonator comprising a side radiation source.

FIG. 21 is an exemplary cross section view of a non-limiting truncatedtapered cavity resonator comprising a substantially flat base andtruncated interior surfaces, and a side radiation source.

FIG. 22 is a non-limiting exemplary plot of a first azimuthaleigenfunction of a conical cavity resonator.

FIG. 23 is a non-limiting exemplary plot of a second azimuthaleigenfunction of a conical cavity resonator.

FIG. 24 is a non-limiting exemplary plot of a first transverse magneticpolar eigenfunction of a conical cavity resonator.

FIG. 25 is a non-limiting exemplary plot of a second transverse magneticpolar eigenfunction of a conical cavity resonator.

FIG. 26 is a non-limiting exemplary plot of a first transverse magneticradial eigenfunction of a conical cavity resonator.

FIG. 27 is a non-limiting exemplary plot of a second transverse magneticradial eigenfunction of a conical cavity resonator.

FIG. 28 is a non-limiting exemplary plot of a first transverse magneticevanescent radial eigenfunction of a conical cavity resonator.

FIG. 29 is a non-limiting exemplary plot of a second transverse magneticevanescent radial eigenfunction of a conical cavity resonator.

FIG. 30 is a non-limiting exemplary plot of a first transverse electricpolar eigenfunction of a conical cavity resonator.

FIG. 31 is a non-limiting exemplary plot of a second transverse electricpolar eigenfunction of a conical cavity resonator.

FIG. 32 is a non-limiting exemplary plot of a first transverse electricradial eigenfunction of a conical cavity resonator.

FIG. 33 is a non-limiting exemplary plot of a second transverse electricradial eigenfunction of a conical cavity resonator.

FIG. 34 is a non-limiting exemplary plot of a first transverse electricevanescent radial eigenfunction of a conical cavity resonator.

FIG. 35 is a non-limiting exemplary plot of a second transverse electricevanescent radial eigenfunction of a conical cavity resonator.

FIG. 36 is a non-limiting exemplary plot of a first azimuthaleigenfunction of a pyramidal cavity resonator.

FIG. 37 is a non-limiting exemplary plot of a second azimuthaleigenfunction of a pyramidal cavity resonator.

FIG. 38 is a non-limiting exemplary plot of a first transverse magneticpolar eigenfunction of a pyramidal cavity resonator.

FIG. 39 is a non-limiting exemplary plot of a second transverse magneticpolar eigenfunction of a pyramidal cavity resonator.

FIG. 40 is a non-limiting exemplary plot of a first transverse magneticradial eigenfunction of a pyramidal cavity resonator.

FIG. 41 is a non-limiting exemplary plot of a second transverse magneticradial eigenfunction of a pyramidal cavity resonator.

FIG. 42 is a non-limiting exemplary plot of a first transverse magneticevanescent radial eigenfunction of a pyramidal cavity resonator.

FIG. 43 is a non-limiting exemplary plot of a second transverse magneticevanescent radial eigenfunction of a pyramidal cavity resonator.

FIG. 44 is a non-limiting exemplary plot of a first transverse electricpolar eigenfunction of a pyramidal cavity resonator.

FIG. 45 is a non-limiting exemplary plot of a second transverse electricpolar eigenfunction of a pyramidal cavity resonator.

FIG. 46 is a non-limiting exemplary plot of a first transverse electricradial eigenfunction of a pyramidal cavity resonator.

FIG. 47 is a non-limiting exemplary plot of a second transverse electricradial eigenfunction of a pyramidal cavity resonator.

FIG. 48 is a non-limiting exemplary plot of a first transverse electricevanescent radial eigenfunction of a pyramidal cavity resonator.

FIG. 49 is a non-limiting exemplary plot of a second transverse electricevanescent radial eigenfunction of a pyramidal cavity resonator.

FIG. 50 is an exemplary perspective view of a first three-dimensionalelectric field vector plot of a non-limiting conical cavity resonator.

FIG. 51 is an exemplary perspective view of a first three-dimensionalmagnetic field vector plot of a non-limiting conical cavity resonator.

FIG. 52 is an exemplary axial cross section view of a first electricfield density plot of a non-limiting conical cavity resonator.

FIG. 53 is an exemplary axial cross section view of a first magneticfield vector plot of a non-limiting conical cavity resonator.

FIG. 54 is an exemplary radial cross section view of a first electricfield vector plot of a non-limiting conical cavity resonator.

FIG. 55 is an exemplary radial cross section view of a first electricfield vector plot of a non-limiting conical cavity resonator comprisinga substantially flat base interior surface.

FIG. 56 is an exemplary radial cross section view of a first magneticfield density plot of a non-limiting conical cavity resonator.

FIG. 57 is an exemplary radial cross section view of a first magneticfield density plot of a non-limiting conical cavity resonator comprisinga substantially flat base interior surface.

FIG. 58 is an exemplary radial cross section view of a first electricfield vector plot of a non-limiting truncated conical cavity resonator.

FIG. 59 is an exemplary radial cross section view of a first electricfield vector plot of a non-limiting truncated conical cavity resonatorcomprising a substantially flat base and truncated interior surfaces.

FIG. 60 is an exemplary radial cross section view of a first magneticfield density plot of a non-limiting truncated conical cavity resonator.

FIG. 61 is an exemplary radial cross section view of a first magneticfield density plot of a non-limiting truncated conical cavity resonatorcomprising a substantially flat base and truncated interior surfaces.

FIG. 62 is an exemplary perspective view of a second three-dimensionalelectric field vector plot of a non-limiting conical cavity resonator.

FIG. 63 is an exemplary perspective view of a second three-dimensionalmagnetic field vector plot of a non-limiting conical cavity resonator.

FIG. 64 is an exemplary axial cross section view of a second electricfield density plot of a non-limiting conical cavity resonator.

FIG. 65 is an exemplary axial cross section view of a second magneticfield vector plot of a non-limiting conical cavity resonator.

FIG. 66 is an exemplary radial cross section view of a second electricfield vector plot of a non-limiting conical cavity resonator.

FIG. 67 is an exemplary radial cross section view of a second electricfield vector plot of a non-limiting conical cavity resonator comprisinga substantially flat base interior surface.

FIG. 68 is an exemplary radial cross section view of a second magneticfield density plot of a non-limiting conical cavity resonator.

FIG. 69 is an exemplary radial cross section view of a second magneticfield density plot of a non-limiting conical cavity resonator comprisinga substantially flat base interior surface.

FIG. 70 is an exemplary radial cross section view of a second electricfield vector plot of a non-limiting truncated conical cavity resonator.

FIG. 71 is an exemplary radial cross section view of a second electricfield vector plot of a non-limiting truncated conical cavity resonatorcomprising a substantially flat base and truncated interior surfaces.

FIG. 72 is an exemplary radial cross section view of a second magneticfield density plot of a non-limiting truncated conical cavity resonator.

FIG. 73 is an exemplary radial cross section view of a second magneticfield density plot of a non-limiting truncated conical cavity resonatorcomprising a substantially flat base and truncated interior surfaces.

FIG. 74 is an exemplary perspective view of a third three-dimensionalelectric field vector plot of a non-limiting conical cavity resonator.

FIG. 75 is an exemplary perspective view of a third three-dimensionalmagnetic field vector plot of a non-limiting conical cavity resonator.

FIG. 76 is an exemplary axial cross section view of a third electricfield vector plot of a non-limiting conical cavity resonator.

FIG. 77 is an exemplary axial cross section view of a third magneticfield vector plot of a non-limiting conical cavity resonator.

FIG. 78 is an exemplary radial cross section view of a third electricfield vector plot of a non-limiting conical cavity resonator.

FIG. 79 is an exemplary radial cross section view of a third electricfield vector plot of a non-limiting conical cavity resonator comprisinga substantially flat base interior surface.

FIG. 80 is an exemplary radial cross section view of a third magneticfield vector plot of a non-limiting conical cavity resonator.

FIG. 81 is an exemplary radial cross section view of a third magneticfield vector plot of a non-limiting conical cavity resonator comprisinga substantially flat base interior surface.

FIG. 82 is an exemplary radial cross section view of a third electricfield vector plot of a non-limiting truncated conical cavity resonator.

FIG. 83 is an exemplary radial cross section view of a third electricfield vector plot of a non-limiting truncated conical cavity resonatorcomprising a substantially flat base and truncated interior surfaces.

FIG. 84 is an exemplary radial cross section view of a third magneticfield vector plot of a non-limiting truncated conical cavity resonator.

FIG. 85 is an exemplary radial cross section view of a third magneticfield vector plot of a non-limiting truncated conical cavity resonatorcomprising a substantially flat base and truncated interior surfaces.

FIG. 86 is an exemplary perspective view of a first three-dimensionalelectric field vector plot of a non-limiting pyramidal cavity resonator.

FIG. 87 is an exemplary perspective view of a first three-dimensionalmagnetic field vector plot of a non-limiting pyramidal cavity resonator.

FIG. 88 is an exemplary axial cross section view of a first electricfield density plot of a non-limiting pyramidal cavity resonator.

FIG. 89 is an exemplary axial cross section view of a first magneticfield vector plot of a non-limiting pyramidal cavity resonator.

FIG. 90 is an exemplary radial cross section view of a first electricfield vector plot of a non-limiting pyramidal cavity resonator.

FIG. 91 is an exemplary radial cross section view of a first electricfield vector plot of a non-limiting pyramidal cavity resonatorcomprising a substantially flat base interior surface.

FIG. 92 is an exemplary radial cross section view of a first magneticfield density plot of a non-limiting pyramidal cavity resonator.

FIG. 93 is an exemplary radial cross section view of a first magneticfield density plot of a non-limiting pyramidal cavity resonatorcomprising a substantially flat base interior surface.

FIG. 94 is an exemplary radial cross section view of a first electricfield vector plot of a non-limiting truncated pyramidal cavityresonator.

FIG. 95 is an exemplary radial cross section view of a first electricfield vector plot of a non-limiting truncated pyramidal cavity resonatorcomprising a substantially flat base and truncated interior surfaces.

FIG. 96 is an exemplary radial cross section view of a first magneticfield density plot of a non-limiting truncated pyramidal cavityresonator.

FIG. 97 is an exemplary radial cross section view of a first magneticfield density plot of a non-limiting truncated pyramidal cavityresonator comprising a substantially flat base and truncated interiorsurfaces.

FIG. 98 is an exemplary perspective view of a second three-dimensionalelectric field vector plot of a non-limiting pyramidal cavity resonator.

FIG. 99 is an exemplary perspective view of a second three-dimensionalmagnetic field vector plot of a non-limiting pyramidal cavity resonator.

FIG. 100 is an exemplary axial cross section view of a second electricfield density plot of a non-limiting pyramidal cavity resonator.

FIG. 101 is an exemplary axial cross section view of a second magneticfield vector plot of a non-limiting pyramidal cavity resonator.

FIG. 102 is an exemplary radial cross section view of a second electricfield vector plot of a non-limiting pyramidal cavity resonator.

FIG. 103 is an exemplary radial cross section view of a second electricfield vector plot of a non-limiting pyramidal cavity resonatorcomprising a substantially flat base interior surface.

FIG. 104 is an exemplary radial cross section view of a second magneticfield density plot of a non-limiting pyramidal cavity resonator.

FIG. 105 is an exemplary radial cross section view of a second magneticfield density plot of a non-limiting pyramidal cavity resonatorcomprising a substantially flat base interior surface.

FIG. 106 is an exemplary radial cross section view of a second electricfield vector plot of a non-limiting truncated pyramidal cavityresonator.

FIG. 107 is an exemplary radial cross section view of a second electricfield vector plot of a non-limiting truncated pyramidal cavity resonatorcomprising a substantially flat base and truncated interior surfaces.

FIG. 108 is an exemplary radial cross section view of a second magneticfield density plot of a non-limiting truncated pyramidal cavityresonator.

FIG. 109 is an exemplary radial cross section view of a second magneticfield density plot of a non-limiting truncated pyramidal cavityresonator comprising a substantially flat base and truncated interiorsurfaces.

FIG. 110 is an exemplary perspective view of a third three-dimensionalelectric field vector plot of a non-limiting pyramidal cavity resonator.

FIG. 111 is an exemplary perspective view of a third three-dimensionalmagnetic field vector plot of a non-limiting pyramidal cavity resonator.

FIG. 112 is an exemplary axial cross section view of a third electricfield density plot of a non-limiting pyramidal cavity resonator.

FIG. 113 is an exemplary axial cross section view of a third magneticfield vector plot of a non-limiting pyramidal cavity resonator.

FIG. 114 is an exemplary radial cross section view of a third electricfield vector plot of a non-limiting pyramidal cavity resonator.

FIG. 115 is an exemplary radial cross section view of a third electricfield vector plot of a non-limiting pyramidal cavity resonatorcomprising a substantially flat base interior surface.

FIG. 116 is an exemplary radial cross section view of a third magneticfield vector plot of a non-limiting pyramidal cavity resonator.

FIG. 117 is an exemplary radial cross section view of a third magneticfield vector plot of a non-limiting pyramidal cavity resonatorcomprising a substantially flat base interior surface.

FIG. 118 is an exemplary radial cross section view of a third electricfield vector plot of a non-limiting truncated pyramidal cavityresonator.

FIG. 119 is an exemplary radial cross section view of a third electricfield vector plot of a non-limiting truncated pyramidal cavity resonatorcomprising a substantially flat base and truncated interior surfaces.

FIG. 120 is an exemplary radial cross section view of a third magneticfield vector plot of a non-limiting truncated pyramidal cavityresonator.

FIG. 121 is an exemplary radial cross section view of a third magneticfield vector plot of a non-limiting truncated pyramidal cavity resonatorcomprising a substantially flat base and truncated interior surfaces.

FIG. 122 is an exemplary perspective view of a non-limitingenvironmental control apparatus.

FIG. 123 is an exemplary cross-section view of a non-limitingenvironmental control apparatus.

DETAILED DESCRIPTION OF THE FIGURES

Disclosed herein, per FIG. 1, is an electromagnetic energy momentumthruster comprising a tapered cavity resonator 10 and an electromagneticradiation source 20 in communication with the cavity resonator 10. Insome embodiments, the electromagnetic radiation source 20 is configuredto emit an electromagnetic wave into the cavity resonator 10. In someembodiments, the electromagnetic radiation source 20 is configured toemit an electromagnetic wave into the cavity resonator 10 via atransmission line 30. In some embodiments, the electromagnetic wave hasa frequency between about 1.0 MHz to about 1000 THz. In someembodiments, the cavity resonator 10 is confined within an environmentalcontrol apparatus 40.

Conical Cavity Resonator Thruster

Provided herein per FIGS. 2, 3, and 10-15 is an electromagnetic energymomentum thruster comprising a conical cavity resonator 100 and a baseelectromagnetic radiation source 600 a or a side electromagneticradiation source 600 b. In some embodiments, the cavity resonator 100forms a cavity 180 having a base interior surface 110 and a taperedinterior surface 120, wherein the tapered interior surface converges toan apex point 130.

In some embodiments, the base electromagnetic radiation source 600 a isconfigured to emit an electromagnetic wave into the cavity 180 having afrequency between about 10{circumflex over ( )}0 MHz to about10{circumflex over ( )}9 MHz. In some embodiments, the sideelectromagnetic radiation source 600 b is configured to emit anelectromagnetic wave into the cavity 180 having a frequency betweenabout 10{circumflex over ( )}0 MHz to about 10{circumflex over ( )}9MHz.

In some embodiments, the base electromagnetic radiation source 600 a isconfigured to produce the frequency of the electromagnetic wave inevanescence, so that the electromagnetic wave has a maximum fieldamplitude and an asymptotic field amplitude. In some embodiments, themaximum field amplitude is at, or adjacent to, the base interior surface110, and the asymptotic field amplitude is at, or adjacent to, one orboth the tapered interior surface 120 and the apex point 130. In someembodiments, the side electromagnetic radiation source 600 b isconfigured to produce the frequency of the electromagnetic wave inevanescence, so that the electromagnetic wave has a maximum fieldamplitude and an asymptotic field amplitude. In some embodiments, themaximum field amplitude is at, or adjacent to, one or both the taperedinterior surface 120 and the apex point 130, and the asymptotic fieldamplitude is at, or adjacent to, the base interior surface 110.

In some embodiments, the cavity 180 includes an overall interior surfacecomprising the base interior surface 110 and the tapered interiorsurface 120. In some embodiments, substantially the entire overallinterior surface of the cavity 180 is electrically conductive. In someembodiments, substantially the entire overall interior surface of thecavity 180 is superconductive. In some embodiments, substantially theentire overall interior surface of the cavity 180 is electricallyconductive, and has a quality factor between about 10{circumflex over( )}3 to about 10{circumflex over ( )}9. In some embodiments,substantially the entire overall interior surface of the cavity 180 issuperconductive, and has a quality factor between about 10{circumflexover ( )}6 to about 10{circumflex over ( )}15.

In some embodiments, substantially the entire overall interior surfaceof the cavity 180 comprises aluminum, antimony, arsenic, barium,beryllium, bismuth, cadmium, calcium, carbon, chromium, cobalt, copper,gallium, gold, hydrogen, indium, iron, lanthanum, lead, lithium,magnesium, manganese, mercury, molybdenum, nickel, niobium, nitrogen,oxygen, palladium, phosphorus, platinum, scandium, silicon, silver,strontium, sulfur, tantalum, technetium, tin, titanium, tungsten,vanadium, yttrium, zinc, zirconium, or any combination thereof. In someembodiments, substantially the entire overall interior surface of thecavity 180 comprises aluminum, barium, beryllium, bismuth, cadmium,calcium, copper, gallium, gadolinium, germanium, lanthanum, lead,lithium, indium, mercury, molybdenum, niobium, nitrogen, osmium, oxygen,protactinium, rhenium, ruthenium, silicon, strontium, sulfur, tantalum,technetium, thallium, thorium, titanium, tin, vanadium, yttrium, zinc,zirconium, NbTi, PbMoS, V₃Ga, NbN, V₃Si, Nb₃Sn, Nb₃Al, Nb₃(AlGe), Nb₃Ge,Bi₂Sr₂CuO₆, Bi₂Sr₂CaCu₂O₈, Bi₂Sr₂Ca₂Cu₃O₁₀, YBa₂Cu₃O₇, YBa₂Cu₄O₈,Y₂Ba₄Cu₇O₁₅, Y₃Ba₅Cu₈O₁₈, Tl₂Ba₂CuO₆, Tl₂Ba₂CaCu₂O₈, Tl₂Ba₂Ca₂Cu₃O₁₀,TlBa₂Ca₃Cu₄O₁₁, HgBa₂CuO₄, HgBa₂CaCu₂O₆, HgBa₂Ca₂Cu₃O₈, or anycombination thereof.

In some embodiments, the cavity 180 is empty. In some embodiments, thecavity 180 comprises a vacuum with a pressure between about10{circumflex over ( )}-24 Torr to about 10{circumflex over ( )}3 Torr.In some embodiments, the cavity 180 comprises a vacuum with a pressureof about 10{circumflex over ( )}-24 Torr, about 10{circumflex over( )}-21 Torr, about 10{circumflex over ( )}-18 Torr, about 10{circumflexover ( )}-15 Torr, about 10{circumflex over ( )}-12 Torr, about10{circumflex over ( )}-9 Torr, about 10{circumflex over ( )}-6 Torr,about 10{circumflex over ( )}-3 Torr, about 1.0 Torr, or about10{circumflex over ( )}3 Torr.

In some embodiments, the cavity 180 comprises a thermal reservoir with atemperature between about 10{circumflex over ( )}-3 Kelvin to about10{circumflex over ( )}3 Kelvin. In some embodiments, the cavity 180comprises a thermal reservoir with a temperature of about 10{circumflexover ( )}-3 Kelvin, about 1 Kelvin, about 5 Kelvin, about 10 Kelvin,about 25 Kelvin, about 50 Kelvin, about 75 Kelvin, about 100 Kelvin,about 150 Kelvin, about 200 Kelvin, about 300 Kelvin, or about10{circumflex over ( )}3 Kelvin.

In some embodiments, the electromagnetic wave comprises a transversemagnetic wave with a polar mode number of N1 and an azimuthal modenumber of N2, where N1 and N2 are an integers from 0 to 1000, and N1 isgreater than or equal to N2. In some embodiments, the electromagneticwave comprises a transverse magnetic wave with a polar mode number of Nand an azimuthal mode number of 0, where N is an integer from 0 to 1000.In some embodiments, the electromagnetic wave comprises a transversemagnetic wave with a polar mode number of N and an azimuthal mode numberof N, where N is an integer from 0 to 1000. In some embodiments, theelectromagnetic wave comprises a transverse electric wave with a polarmode number of N1 and an azimuthal mode number of N2, where N1 and N2are an integers from 0 to 1000, and N1 is greater than or equal to N2.In some embodiments, the electromagnetic wave comprises a transverseelectric wave with a polar mode number of N and an azimuthal mode numberof 0, where N is an integer from 0 to 1000. In some embodiments, theelectromagnetic wave comprises a transverse electric wave with a polarmode number of N and an azimuthal mode number of N, where N is aninteger from 0 to 1000. In some embodiments, the electromagneticradiation source is located inside the cavity 180 at, or adjacent to, amaximum field amplitude of the electromagnetic wave.

In some embodiments, the cavity 180 has at least one of a width 140 anda height 150 between about 10{circumflex over ( )}-9 meters to about10{circumflex over ( )}3 meters. In some embodiments, the width 140 ismeasured as a maximum diameter of the base interior surface 110. In someembodiments, the height 150 is measured as a distance from the baseinterior surface 110 to the apex point 130. In some embodiments, thetapered interior surface 120 forms an aperture angle 160 between about 5degrees to about 175 degrees. In some embodiments, the aperture angle160 is measured as the interior angle of the tapered interior surface120 at the apex point 130. In some embodiments, the cavity 180 has awall with a wall thickness 170 between about 10{circumflex over ( )}-9meters to about 1.0 meter. In some embodiments, the wall thickness 170is measured as a normal distance between the overall interior surface ofthe cavity 180 and an exterior of the cavity resonator 100. In someembodiments, the base interior surface 110 has a different wallthickness 170 than the tapered interior surface 120. In someembodiments, the base interior surface 110 has about the same wallthickness 170 as the tapered interior surface 120.

In some embodiments, the base interior surface 110 is substantiallyelliptical. In some embodiments, the base interior surface 110 issubstantially circular. In some embodiments, the base interior surface110 is substantially flat.

In some embodiments, the electromagnetic wave forms an electromagneticenergy momentum tensor with an amplitude maximum at, or adjacent to, thebase interior surface 110, which results in one or more of a metrictensor curvature, a thrust, and an acceleration of the thruster. In someembodiments, the electromagnetic wave forms an electromagnetic energymomentum tensor with an amplitude maximum at, or adjacent to, one orboth the tapered interior surface 120 and the apex point 130, whichresults in one or more of a metric tensor curvature, a thrust, and anacceleration of the thruster.

Truncated Conical Cavity Resonator Thruster

Provided herein per FIGS. 4, 5, and 16-21 is an electromagnetic energymomentum thruster comprising a truncated conical cavity resonator 200and a base electromagnetic radiation source 600 a or a sideelectromagnetic radiation source 600 b. In some embodiments, the cavityresonator 200 forms a cavity 280 having a base interior surface 210, atapered interior surface 220, and a truncated interior surface 230opposing the base interior surface 210, the tapered interior surface 220being between the base interior surface 210 and the truncated interiorsurface 230.

In some embodiments, the base electromagnetic radiation source 600 a isconfigured to emit an electromagnetic wave into the cavity 280 having afrequency between about 10{circumflex over ( )}0 MHz to about10{circumflex over ( )}9 MHz. In some embodiments, the sideelectromagnetic radiation source 600 b is configured to emit anelectromagnetic wave into the cavity 280 having a frequency betweenabout 10{circumflex over ( )}0 MHz to about 10{circumflex over ( )}9MHz.

In some embodiments, the base electromagnetic radiation source 600 a isconfigured to produce the electromagnetic wave in evanescence so thatthe electromagnetic wave has a maximum field amplitude and an asymptoticfield amplitude. In some embodiments, the maximum field amplitude is at,or adjacent to, the base interior surface 210, and the asymptotic fieldamplitude is at, or adjacent to, one or both the tapered interiorsurface 220 and the truncated interior surface 230. In some embodiments,the side electromagnetic radiation source 600 b is configured to producethe electromagnetic wave in evanescence so that the electromagnetic wavehas a maximum field amplitude and an asymptotic field amplitude. In someembodiments, the maximum field amplitude is at, or adjacent to, one orboth the tapered interior surface 220 and the truncated interior surface230, and the asymptotic field amplitude is at, or adjacent to, the baseinterior surface 210.

In some embodiments, the cavity 280 includes an overall interior surfacecomprising the base interior surface 210, the tapered interior surface220, and the truncated interior surface 230. In some embodiments,substantially the entire overall interior surface of the cavity 280 iselectrically conductive. In some embodiments, substantially the entireoverall interior surface of the cavity 280 is superconductive. In someembodiments, substantially the entire overall interior surface of thecavity 280 is electrically conductive, and has a quality factor betweenabout 10{circumflex over ( )}3 to about 10{circumflex over ( )}9. Insome embodiments, substantially the entire overall interior surface ofthe cavity 280 is superconductive, and has a quality factor betweenabout 10{circumflex over ( )}6 to about 10{circumflex over ( )}15.

In some embodiments, substantially the entire overall interior surfaceof the cavity 280 comprises aluminum, antimony, arsenic, barium,beryllium, bismuth, cadmium, calcium, carbon, chromium, cobalt, copper,gallium, gold, hydrogen, indium, iron, lanthanum, lead, lithium,magnesium, manganese, mercury, molybdenum, nickel, niobium, nitrogen,oxygen, palladium, phosphorus, platinum, scandium, silicon, silver,strontium, sulfur, tantalum, technetium, tin, titanium, tungsten,vanadium, yttrium, zinc, zirconium, or any combination thereof. In someembodiments, substantially the entire overall interior surface of thecavity 280 comprises aluminum, barium, beryllium, bismuth, cadmium,calcium, copper, gallium, gadolinium, germanium, lanthanum, lead,lithium, indium, mercury, molybdenum, niobium, nitrogen, osmium, oxygen,protactinium, rhenium, ruthenium, silicon, strontium, sulfur, tantalum,technetium, thallium, thorium, titanium, tin, vanadium, yttrium, zinc,zirconium, NbTi, PbMoS, V₃Ga, NbN, V₃Si, Nb₃Sn, Nb₃Al, Nb₃(AlGe), Nb₃Ge,Bi₂Sr₂CuO₆, Bi₂Sr₂CaCu₂O₈, Bi₂Sr₂Ca₂Cu₃O₁₀, YBa₂Cu₃O₇, YBa₂Cu₄O₈,Y₂Ba₄Cu₇O₁₅, Y₃Ba₅Cu₈O₁₈, Tl₂Ba₂CuO₆, Tl₂Ba₂CaCu₂O₈, Tl₂Ba₂Ca₂Cu₃O₁₀,TlBa₂Ca₃Cu₄O₁₁, HgBa₂CuO₄, HgBa₂CaCu₂O₆, HgBa₂Ca₂Cu₃O₈, or anycombination thereof.

In some embodiments, the cavity 280 is empty. In some embodiments, thecavity 280 comprises a vacuum with a pressure between about10{circumflex over ( )}-24 Torr to about 10{circumflex over ( )}3 Torr.In some embodiments, the cavity 280 comprises a vacuum with a pressureof about 10{circumflex over ( )}-24 Torr, about 10{circumflex over( )}-21 Torr, about 10{circumflex over ( )}-18 Torr, about 10{circumflexover ( )}-15 Torr, about 10{circumflex over ( )}-12 Torr, about10{circumflex over ( )}-9 Torr, about 10{circumflex over ( )}-6 Torr,about 10{circumflex over ( )}-3 Torr, about 1.0 Torr, or about10{circumflex over ( )}3 Torr.

In some embodiments, the cavity 280 comprises a thermal reservoir with atemperature between about 10{circumflex over ( )}-3 Kelvin to about10{circumflex over ( )}3 Kelvin. In some embodiments, the cavity 280comprises a thermal reservoir with a temperature of about 10{circumflexover ( )}-3 Kelvin, about 1 Kelvin, about 5 Kelvin, about 10 Kelvin,about 25 Kelvin, about 50 Kelvin, about 75 Kelvin, about 100 Kelvin,about 150 Kelvin, about 200 Kelvin, about 300 Kelvin, or about10{circumflex over ( )}3 Kelvin.

In some embodiments, the electromagnetic wave comprises a transversemagnetic wave with a polar mode number of N1 and an azimuthal modenumber of N2, where N1 and N2 are an integers from 0 to 1000, and N1 isgreater than or equal to N2. In some embodiments, the electromagneticwave comprises a transverse magnetic wave with a polar mode number of Nand an azimuthal mode number of 0, where N is an integer from 0 to 1000.In some embodiments, the electromagnetic wave comprises a transversemagnetic wave with a polar mode number of N and an azimuthal mode numberof N, where N is an integer from 0 to 1000. In some embodiments, theelectromagnetic wave comprises a transverse electric wave with a polarmode number of N1 and an azimuthal mode number of N2, where N1 and N2are an integers from 0 to 1000, and N1 is greater than or equal to N2.In some embodiments, the electromagnetic wave comprises a transverseelectric wave with a polar mode number of N and an azimuthal mode numberof 0, where N is an integer from 0 to 1000.

In some embodiments, the electromagnetic wave comprises a transverseelectric wave with a polar mode number of N and an azimuthal mode numberof N, where N is an integer from 0 to 1000. In some embodiments, theelectromagnetic radiation source is located inside the cavity 280 at, oradjacent to, a maximum field amplitude of the electromagnetic wave.

In some embodiments, the cavity 280 has at least one of a width 240 anda height 250 between about 10{circumflex over ( )}-9 meters to about10{circumflex over ( )}3 meters. In some embodiments, the width 240 ismeasured as a maximum diameter of the base interior surface 210. In someembodiments, the height 250 is measured as a normal distance from thebase interior surface 210 to the truncated interior surface 230. In someembodiments, the tapered interior surface 220 forms an aperture angle260 between about 5 degrees to about 175 degrees. In some embodiments,the aperture angle 260 is measured as the interior angle of the taperedinterior surface 220. In some embodiments, the cavity 280 has a wallwith a wall thickness 270 between about 10{circumflex over ( )}-9 metersto about 1.0 meter. In some embodiments, the wall thickness 270 ismeasured as a normal distance between the overall interior surface ofthe cavity 280 and an exterior of the cavity resonator 200. In someembodiments, the base interior surface 210 has a different wallthickness 270 than the tapered interior surface 220. In someembodiments, the base interior surface 210 has about the same wallthickness 270 as the tapered interior surface 220. In some embodiments,the truncated interior surface 230 has a different wall thickness 270than the tapered interior surface 220. In some embodiments, thetruncated interior surface 230 has about the same wall thickness 270 thetapered interior surface 220. In some embodiments, the base interiorsurface 210 has a different wall thickness 270 than the truncatedinterior surface 230. In some embodiments, the base interior surface 210has about the same wall thickness 270 as the truncated interior surface230.

In some embodiments, one or both the base interior surface 210 and thetruncated interior surface 230 is substantially elliptical. In someembodiments, one or both the base interior surface 210 and the truncatedinterior surface 230 is substantially circular. In some embodiments, oneor both the base interior surface 210 and the truncated interior surface230 is substantially flat.

In some embodiments, the electromagnetic wave forms an electromagneticenergy momentum tensor with an amplitude maximum at, or adjacent to, thebase interior surface 210, which results in one or more of a metrictensor curvature, a thrust, and an acceleration of the thruster. In someembodiments, the electromagnetic wave forms an electromagnetic energymomentum tensor with an amplitude maximum at, or adjacent to, one orboth the tapered interior surface 220 and the truncated interior surface230, which results in one or more of a metric tensor curvature, athrust, and an acceleration of the thruster.

Pyramidal Cavity Resonator Thruster

Provided herein per FIGS. 6, 7, and 10-15 is an electromagnetic energymomentum thruster comprising a pyramidal cavity resonator 300 and a baseelectromagnetic radiation source 600 a or a side electromagneticradiation source 600 b. In some embodiments, the cavity resonator 300forms a cavity 380 having a base interior surface 310 and at least threetapered interior surfaces 320, the tapered interior surfaces 320converging to an apex point 330.

In some embodiments, the base electromagnetic radiation source 600 a isconfigured to emit an electromagnetic wave into the cavity 380 having afrequency between about 10{circumflex over ( )}0 MHz to about10{circumflex over ( )}9 MHz. In some embodiments, the sideelectromagnetic radiation source 600 b is configured to emit anelectromagnetic wave into the cavity 380 having a frequency betweenabout 10{circumflex over ( )}0 MHz to about 10{circumflex over ( )}9MHz.

In some embodiments, the base electromagnetic radiation source 600 a isconfigured to produce the frequency of the electromagnetic wave inevanescence so that the electromagnetic wave has a maximum fieldamplitude and an asymptotic field amplitude. In some embodiments, themaximum field amplitude is at, or adjacent to, the base interior surface310, and the asymptotic field amplitude is at, or adjacent to, one ormore of the at least three tapered interior surfaces 320 and the apexpoint 330. In some embodiments, the side electromagnetic radiationsource 600 b is configured to produce the frequency of theelectromagnetic wave in evanescence so that the electromagnetic wave hasa maximum field amplitude and an asymptotic field amplitude. In someembodiments, the maximum field amplitude is at, or adjacent to, one ormore of the at least three tapered interior surfaces 320 and the apexpoint 330, and the asymptotic field amplitude is at, or adjacent to, thebase interior surface 310.

In some embodiments, the cavity 380 includes an overall interior surfacecomprising the base interior surface 310 and the at least three taperedinterior surfaces 320. In some embodiments, substantially the entireoverall interior surface of the cavity 380 is electrically conductive.In some embodiments, substantially the entire overall interior surfaceof the cavity 380 is superconductive. In some embodiments, substantiallythe entire overall interior surface of the cavity 380 is electricallyconductive, and has a quality factor between about 10{circumflex over( )}3 to about 10{circumflex over ( )}9. In some embodiments,substantially the entire overall interior surface of the cavity 380 issuperconductive, and has a quality factor between about 10{circumflexover ( )}6 to about 10{circumflex over ( )}15.

In some embodiments, substantially the entire overall interior surfaceof the cavity 380 comprises aluminum, antimony, arsenic, barium,beryllium, bismuth, cadmium, calcium, carbon, chromium, cobalt, copper,gallium, gold, hydrogen, indium, iron, lanthanum, lead, lithium,magnesium, manganese, mercury, molybdenum, nickel, niobium, nitrogen,oxygen, palladium, phosphorus, platinum, scandium, silicon, silver,strontium, sulfur, tantalum, technetium, tin, titanium, tungsten,vanadium, yttrium, zinc, zirconium, or any combination thereof. In someembodiments, substantially the entire overall interior surface of thecavity 380 comprises aluminum, barium, beryllium, bismuth, cadmium,calcium, copper, gallium, gadolinium, germanium, lanthanum, lead,lithium, indium, mercury, molybdenum, niobium, nitrogen, osmium, oxygen,protactinium, rhenium, ruthenium, silicon, strontium, sulfur, tantalum,technetium, thallium, thorium, titanium, tin, vanadium, yttrium, zinc,zirconium, NbTi, PbMoS, V₃Ga, NbN, V₃Si, Nb₃Sn, Nb₃Al, Nb₃(AlGe), Nb₃Ge,Bi₂Sr₂CuO₆, Bi₂Sr₂CaCu₂O₈, Bi₂Sr₂Ca₂Cu₃O₁₀, YBa₂Cu₃O₇, YBa₂Cu₄O₈,Y₂Ba₄Cu₇O₁₅, Y₃Ba₅Cu₈O₁₈, Tl₂Ba₂CuO₆, Tl₂Ba₂CaCu₂O₈, Tl₂Ba₂Ca₂Cu₃O₁₀,TlBa₂Ca₃Cu₄O₁₁, HgBa₂CuO₄, HgBa₂CaCu₂O₆, HgBa₂Ca₂Cu₃O₈, or anycombination thereof.

In some embodiments, the cavity 380 is empty. In some embodiments, thecavity 380 comprises a vacuum with a pressure between about10{circumflex over ( )}-24 Torr to about 10{circumflex over ( )}3 Torr.In some embodiments, the cavity 380 comprises a vacuum with a pressureof about 10{circumflex over ( )}-24 Torr, about 10{circumflex over( )}-21 Torr, about 10{circumflex over ( )}-18 Torr, about 10{circumflexover ( )}-15 Torr, about 10{circumflex over ( )}-12 Torr, about10{circumflex over ( )}-9 Torr, about 10{circumflex over ( )}-6 Torr,about 10{circumflex over ( )}-3 Torr, about 1.0 Torr, or about10{circumflex over ( )}3 Torr.

In some embodiments, the cavity 380 comprises a thermal reservoir with atemperature between about 10{circumflex over ( )}-3 Kelvin to about10{circumflex over ( )}3 Kelvin. In some embodiments, the cavity 380comprises a thermal reservoir with a temperature of about 10{circumflexover ( )}-3 Kelvin, about 1 Kelvin, about 5 Kelvin, about 10 Kelvin,about 25 Kelvin, about 50 Kelvin, about 75 Kelvin, about 100 Kelvin,about 150 Kelvin, about 200 Kelvin, about 300 Kelvin, or about10{circumflex over ( )}3 Kelvin.

In some embodiments, the electromagnetic wave comprises a transversemagnetic wave with a polar mode number of N1 and an azimuthal modenumber of N2, where N1 and N2 are an integers from 0 to 1000, and N1 isgreater than or equal to N2. In some embodiments, the electromagneticwave comprises a transverse magnetic wave with a polar mode number of Nand an azimuthal mode number of 0, where N is an integer from 0 to 1000.In some embodiments, the electromagnetic wave comprises a transversemagnetic wave with a polar mode number of N and an azimuthal mode numberof N, where N is an integer from 0 to 1000. In some embodiments, theelectromagnetic wave comprises a transverse electric wave with a polarmode number of N1 and an azimuthal mode number of N2, where N1 and N2are an integers from 0 to 1000, and N1 is greater than or equal to N2.In some embodiments, the electromagnetic wave comprises a transverseelectric wave with a polar mode number of N and an azimuthal mode numberof 0, where N is an integer from 0 to 1000. In some embodiments, theelectromagnetic wave comprises a transverse electric wave with a polarmode number of N and an azimuthal mode number of N, where N is aninteger from 0 to 1000. In some embodiments, the electromagneticradiation source is located inside the cavity 380 at, or adjacent to, amaximum field amplitude of the electromagnetic wave.

In some embodiments, the cavity 380 has at least one of a width 340 anda height 350 between about 10{circumflex over ( )}-9 meters to about10{circumflex over ( )}3 meters. In some embodiments, the width 340 ismeasured as a maximum diameter of the base interior surface 310. In someembodiments, the height 350 is measured as a distance from the baseinterior surface 310 to the apex point 330. In some embodiments, two ormore of the at least three tapered interior surfaces 320 form anaperture angle 360 between about 5 degrees to about 175 degrees. In someembodiments, the aperture angle 360 is measured as an internal anglebetween two or more of the at least three tapered interior surfaces 320at the apex point 330. In some embodiments, the cavity has a wall with awall thickness 370 between about 10{circumflex over ( )}-9 meters toabout 1.0 meter. In some embodiments, the wall thickness 370 is measuredas a normal distance between the overall interior surface of the cavity380 and an exterior of the cavity resonator 300. In some embodiments,the base interior surface 310 has a different wall thickness 370 than asat least one of the at least three the tapered interior surfaces 320. Insome embodiments, the base interior surface 310 has about the same wallthickness 370 as at least one of the at least three the tapered interiorsurfaces 320.

In some embodiments, the base interior surface 310 comprises 3, 4, 5, 6,7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, ormore sides. In some embodiments the base interior surface 310 issubstantially equilateral. In some embodiments, the base interiorsurface 310 is substantially flat.

In some embodiments, the electromagnetic wave forms an electromagneticenergy momentum tensor with an amplitude maximum at, or adjacent to, thebase interior surface 310, which results in one or more of a metrictensor curvature, a thrust, and an acceleration of the thruster. In someembodiments, the electromagnetic wave forms an electromagnetic energymomentum tensor with an amplitude maximum at, or adjacent to, one ormore of the at least three tapered interior surfaces 320 and the apexpoint 330, which results in one or more of a metric tensor curvature, athrust, and an acceleration of the thruster.

Truncated Pyramidal Cavity Resonator Thruster

Provided herein per FIGS. 8, 9, and 16-21 is an electromagnetic energymomentum thruster comprising a truncated pyramidal cavity resonator 400and a base electromagnetic radiation source 600 a or a sideelectromagnetic radiation source 600 b. In some embodiments, the cavityresonator 400 forms a cavity 480 having a base interior surface 410, atleast three tapered interior surfaces 420, and a truncated interiorsurface 430 opposing the base interior surface 410, the at least threetapered interior surfaces 420 being between the base interior surface410 and truncated interior surfaces 430.

In some embodiments, the base electromagnetic radiation source 600 a isconfigured to emit an electromagnetic wave into the cavity 480 having afrequency between about 10{circumflex over ( )}0 MHz to about10{circumflex over ( )}9 MHz. In some embodiments, the sideelectromagnetic radiation source 600 b is configured to emit anelectromagnetic wave into the cavity 480 having a frequency betweenabout 10{circumflex over ( )}0 MHz to about 10{circumflex over ( )}9MHz.

In some embodiments, the base electromagnetic radiation source 600 a isconfigured to produce the frequency of the electromagnetic wave inevanescence so that the electromagnetic wave has a maximum fieldamplitude and an asymptotic field amplitude. In some embodiments, themaximum field amplitude is at, or adjacent to, the base interior surface410, and the asymptotic field amplitude is at, or adjacent to, one ormore of the at least three tapered interior surfaces 420 and thetruncated interior surface 430. In some embodiments, the sideelectromagnetic radiation source 600 b is configured to produce thefrequency of the electromagnetic wave in evanescence so that theelectromagnetic wave has a maximum field amplitude and an asymptoticfield amplitude. In some embodiments, the maximum field amplitude is at,or adjacent to, one or more of the at least three tapered interiorsurfaces 420 and the truncated interior surface 430, and the asymptoticfield amplitude is at, or adjacent to, the base interior surface 410.

In some embodiments, the cavity 480 includes an overall interior surfacecomprising the base interior surface 410, the at least three taperedinterior surfaces 420, and the truncated interior surface 430. In someembodiments, substantially the entire overall interior surface of thecavity 480 is electrically conductive. In some embodiments,substantially the entire overall interior surface of the cavity 480 issuperconductive. In some embodiments, substantially the entire overallinterior surface of the cavity 480 is electrically conductive, and has aquality factor between about 10{circumflex over ( )}3 to about10{circumflex over ( )}9. In some embodiments, the entire overallinterior surface of the cavity 480 is superconductive, and has a qualityfactor between about 10{circumflex over ( )}6 to about 10{circumflexover ( )}15.

In some embodiments, substantially the entire overall interior surfaceof the cavity 480 comprises aluminum, antimony, arsenic, barium,beryllium, bismuth, cadmium, calcium, carbon, chromium, cobalt, copper,gallium, gold, hydrogen, indium, iron, lanthanum, lead, lithium,magnesium, manganese, mercury, molybdenum, nickel, niobium, nitrogen,oxygen, palladium, phosphorus, platinum, scandium, silicon, silver,strontium, sulfur, tantalum, technetium, tin, titanium, tungsten,vanadium, yttrium, zinc, zirconium, or any combination thereof. In someembodiments, substantially the entire overall interior surface of thecavity 480 comprises aluminum, barium, beryllium, bismuth, cadmium,calcium, copper, gallium, gadolinium, germanium, lanthanum, lead,lithium, indium, mercury, molybdenum, niobium, nitrogen, osmium, oxygen,protactinium, rhenium, ruthenium, silicon, strontium, sulfur, tantalum,technetium, thallium, thorium, titanium, tin, vanadium, yttrium, zinc,zirconium, NbTi, PbMoS, V₃Ga, NbN, V₃Si, Nb₃Sn, Nb₃Al, Nb₃(AlGe), Nb₃Ge,Bi₂Sr₂CuO₆, Bi₂Sr₂CaCu₂O₈, Bi₂Sr₂Ca₂Cu₃O₁₀, YBa₂Cu₃O₇, YBa₂Cu₄O₈,Y₂Ba₄Cu₇O₁₅, Y₃Ba₅Cu₈O₁₈, Tl₂Ba₂CuO₆, Tl₂Ba₂CaCu₂O₈, Tl₂Ba₂Ca₂Cu₃O₁₀,TlBa₂Ca₃Cu₄O₁₁, HgBa₂CuO₄, HgBa₂CaCu₂O₆, HgBa₂Ca₂Cu₃O₈, or anycombination thereof.

In some embodiments, the cavity 480 is empty. In some embodiments, thecavity 480 comprises a vacuum with a pressure between about10{circumflex over ( )}-24 Torr to about 10{circumflex over ( )}3 Torr.In some embodiments, the cavity 480 comprises a vacuum with a pressureof about 10{circumflex over ( )}-24 Torr, about 10{circumflex over( )}-21 Torr, about 10{circumflex over ( )}-18 Torr, about 10{circumflexover ( )}-15 Torr, about 10{circumflex over ( )}-12 Torr, about10{circumflex over ( )}-9 Torr, about 10{circumflex over ( )}-6 Torr,about 10{circumflex over ( )}-3 Torr, about 1.0 Torr, or about10{circumflex over ( )}3 Torr.

In some embodiments, the cavity 480 comprises a thermal reservoir with atemperature between about 10{circumflex over ( )}-3 Kelvin to about10{circumflex over ( )}3 Kelvin. In some embodiments, the cavity 480comprises a thermal reservoir with a temperature of about 10{circumflexover ( )}-3 Kelvin, about 1 Kelvin, about 5 Kelvin, about 10 Kelvin,about 25 Kelvin, about 50 Kelvin, about 75 Kelvin, about 100 Kelvin,about 150 Kelvin, about 200 Kelvin, about 300 Kelvin, or about10{circumflex over ( )}3 Kelvin.

In some embodiments, the electromagnetic wave comprises a transversemagnetic wave with a polar mode number of N1 and an azimuthal modenumber of N2, where N1 and N2 are an integers from 0 to 1000, and N1 isgreater than or equal to N2. In some embodiments, the electromagneticwave comprises a transverse magnetic wave with a polar mode number of Nand an azimuthal mode number of 0, where N is an integer from 0 to 1000.In some embodiments, the electromagnetic wave comprises a transversemagnetic wave with a polar mode number of N and an azimuthal mode numberof N, where N is an integer from 0 to 1000. In some embodiments, theelectromagnetic wave comprises a transverse electric wave with a polarmode number of N1 and an azimuthal mode number of N2, where N1 and N2are an integers from 0 to 1000, and N1 is greater than or equal to N2.In some embodiments, the electromagnetic wave comprises a transverseelectric wave with a polar mode number of N and an azimuthal mode numberof 0, where N is an integer from 0 to 1000. In some embodiments, theelectromagnetic wave comprises a transverse electric wave with a polarmode number of N and an azimuthal mode number of N, where N is aninteger from 0 to 1000. In some embodiments, the electromagneticradiation source is located inside the cavity 480 at, or adjacent to, amaximum field amplitude of the electromagnetic wave.

In some embodiments, the cavity 480 has at least one of a width 440 anda height 450 between about 10{circumflex over ( )}-9 meters to about10{circumflex over ( )}3 meters. In some embodiments, the width 440 ismeasured as a normal width of the base interior surface 410. In someembodiments, the height 450 is measured as a normal distance from thebase interior surface 410 to the truncated interior surface 430. In someembodiments, two or more of the at least three tapered interior surfaces420 form an aperture angle 460 between about 5 degrees to about 175degrees. In some embodiments, the aperture angle 460 is measured as aninternal angle between two or more of the at least three taperedinterior surfaces 420. In some embodiments, the cavity 480 has a wallwith a wall thickness 470 between about 10{circumflex over ( )}-9 metersto about 1.0 meter. In some embodiments, the wall thickness 470 ismeasured as a normal distance between the overall interior surface ofthe cavity 480 and an exterior of the cavity resonator 400. In someembodiments, the base interior surface 410 has a different wallthickness 470 than at least one of the three or more tapered interiorsurfaces 420. In some embodiments, the base interior surface 410 hasabout the same wall thickness 470 as at least one of the three or moretapered interior surfaces 420. In some embodiments, the truncatedinterior surface 430 has a different wall thickness 470 than at leastone of the three or more tapered interior surfaces 420. In someembodiments, the truncated interior surface 430 has about the same wallthickness 470 as at least one of the three or more tapered interiorsurfaces 420. In some embodiments, the base interior surface 410 has adifferent wall thickness 470 than the truncated interior surface 430. Insome embodiments, the base interior surface 410 has about the same wallthickness 470 as the truncated interior surface 430.

In some embodiments, one or both the base interior surface 410 and thetruncated interior surface 430 comprises 3, 4, 5, 6, 7, 8, 9, 10, 11,12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, or more sides. Insome embodiments, one or both the base interior surface 410 and thetruncated interior surface 430 is substantially equilateral. In someembodiments, one or both the base interior surface 410 and the truncatedinterior surface 430 is substantially flat.

In some embodiments, the electromagnetic wave forms an electromagneticenergy momentum tensor with an amplitude maximum at, or adjacent to, thebase interior surface 410, which results in one or more of a metrictensor curvature, a thrust, and an acceleration of the thruster. In someembodiments, the electromagnetic wave forms an electromagnetic energymomentum tensor with an amplitude maximum at, or adjacent to, one ormore of the at least three tapered interior surfaces 420 and thetruncated interior surface 430, which results in one or more of a metrictensor curvature, a thrust, and an acceleration of the thruster.

Electromagnetic Radiation Source

Provided herein is an electromagnetic energy momentum thrustercomprising a cavity resonator forming a cavity, and an electromagneticradiation source.

In some embodiments, per FIGS. 12 and 13, the electromagnetic energymomentum thruster comprises a tapered cavity resonator 500 and a baseelectromagnetic radiation source 600 a. In some embodiments, per FIGS.14 and 15, the electromagnetic energy momentum thruster comprises atapered cavity resonator 500 and a side electromagnetic radiation source600 b.

In some embodiments, per FIGS. 18 and 19, the electromagnetic energymomentum thruster comprises a truncated tapered cavity resonator 550 anda base electromagnetic radiation source 600 a. In some embodiments, perFIGS. 20 and 21, the electromagnetic energy momentum thruster comprisesa truncated tapered cavity resonator 550 and a side electromagneticradiation source 600 b.

In some embodiments, the tapered cavity resonator 500 comprises apyramidal or a conical cavity resonator. In some embodiments, thetruncated tapered cavity resonator 550 comprises a truncated pyramidalor a truncated conical cavity resonator.

In some embodiments, the base radiation source 600 a emits theelectromagnetic wave from the base interior surface of the taperedcavity resonator 500 or the truncated tapered cavity resonator 550. Insome embodiments, the base radiation source 600 a is affixed to the baseinterior surface of the tapered cavity resonator 500 or the truncatedtapered cavity resonator 550. In some embodiments, the side radiationsource 600 b emits the electromagnetic wave from the tapered interiorsurface of the tapered cavity resonator 500 or the truncated taperedcavity resonator 550. In some embodiments, the side radiation source 600b is affixed to the tapered interior surface of the tapered cavityresonator 500 or the truncated tapered cavity resonator 550.

In some embodiments, the base electromagnetic radiation source 600 a isconfigured to emit an electromagnetic wave into the cavity resonatorhaving a frequency between about 10{circumflex over ( )}0 MHz to about10{circumflex over ( )}9 MHz. In some embodiments, the sideelectromagnetic radiation source 600 b is configured to emit anelectromagnetic wave into the cavity resonator having a frequencybetween about 10{circumflex over ( )}0 MHz to about 10{circumflex over( )}9 MHz.

Environmental Control Apparatus

Provided herein, per FIGS. 122 and 123, is an exemplary environmentalcontrol apparatus 1000. In some embodiments, the environmental controlapparatus 1000 comprises a transmission line 1001, an instrumentationchannel 1002, a coolant input 1003, and a coolant output 1004. In someembodiments, the coolant comprises a gaseous coolant, a liquid coolant,a cryogen coolant, or any combination thereof.

In some embodiments, the exemplary environmental control apparatus 1000comprises at least one of a clamp, a clasp, a cam, a handle, a gasket,an insulator, and a probe.

EXAMPLES

The following illustrative examples are representative of embodiments ofthe hardware applications, systems, and methods described herein and arenot meant to be limiting in any way. Exemplary plots of the transversemagnetic waves and the transverse electric waves of a non-limitingconical cavity resonator, a non-limiting truncated conical cavityresonator, a non-limiting pyramidal cavity resonator, and a non-limitingtruncated pyramidal cavity resonator are shown in FIGS. 22-121.

Example 1—Transverse Electric Wave Frequency of a Conical CavityResonator

In some embodiments, a frequency of a hollow conical cavity resonator iscalculated per the equations below:

For an azimuthal eigenvalue (m) of the resonator:

m=n where n=0,1,2, . . .

For a polar eigenvalue (l), an azimuthal eigenvalue (m), a taper angle(θ₀), and a polar wave equation (P_(l) ^(m)(cos θ)) of the resonator:

$\left\lbrack {\frac{d}{d\; \theta}\left\lbrack {P_{l}^{m}\left( {\cos \mspace{11mu} \theta} \right)} \right\rbrack} \right\rbrack_{\theta = \theta_{0}} = 0$

For a radial eigenvalue (k), a polar eigenvalue (l), a radial length(r₁), and a radial wave equation (j_(l)(kr)) of the resonator:

[(kr)j _(l)(kr)]_(r=0)=0 and [(kr)j _(l)(kr)]_(r=r) ₁ =0

For a radial eigenvalue (k), a polar eigenvalue (l), a radial length(r₁), and a radial wave equation (j_(l)(kr)) of the resonator:

$\left\lbrack {\frac{d}{dr}\left\lbrack {({kr}){j_{l}({kr})}} \right\rbrack} \right\rbrack_{r = 0} = {{0\mspace{14mu} {{or}\mspace{14mu}\left\lbrack {\frac{d}{dr}\left\lbrack {({kr}){j_{l}({kr})}} \right\rbrack} \right\rbrack}_{r = r_{1}}} = 0}$

For a frequency (f), a radial eigenvalue (k), and a speed of light (c)of the resonator:

$f = \frac{kc}{2\pi}$

FIGS. 22 and 23 are non-limiting exemplary plots of a first and a secondazimuthal eigenfunction of a conical cavity resonator, respectively.FIGS. 30 and 31 are non-limiting exemplary plots of a first and a secondtransverse electric polar eigenfunction of a conical cavity resonator,respectively. FIGS. 32 and 33 are non-limiting exemplary plots of afirst and a second transverse electric radial eigenfunction of a conicalcavity resonator, respectively. FIGS. 34 and 35 are non-limitingexemplary plots of a first and a second transverse electric evanescentradial eigenfunction of a conical cavity resonator, respectively.

FIG. 74 is an exemplary perspective view of a first transverse electricthree-dimensional electric field vector plot of a non-limiting conicalcavity resonator. FIG. 75 is an exemplary perspective view of a firsttransverse electric three-dimensional magnetic field vector plot of anon-limiting conical cavity resonator.

FIG. 76 is an exemplary axial cross section view of a first electricfield transverse electric vector plot of a non-limiting conical cavityresonator. FIG. 77 is an exemplary axial cross section view of a firstmagnetic field transverse electric vector plot of a non-limiting conicalcavity resonator.

FIG. 78 is an exemplary radial cross section view of a first electricfield transverse electric vector plot of a non-limiting conical cavityresonator. FIG. 79 is an exemplary radial cross section view of a firstelectric field transverse electric vector plot of a non-limiting conicalcavity resonator comprising a substantially flat base interior surface.

FIG. 80 is an exemplary radial cross section view of a first magneticfield transverse electric vector plot of a non-limiting conical cavityresonator. FIG. 81 is an exemplary radial cross section view of a firstmagnetic field transverse electric vector plot of a non-limiting conicalcavity resonator comprising a substantially flat base interior surface.

As the size of the arrows in the above figures are positively correlatedwith an electric field and an electric field density, or with a magneticfield and a magnetic field density, the non-limiting conical cavityresonator exhibits one or both a highly asymmetric electric field and ahighly asymmetric electric field density, and a highly asymmetricmagnetic field and a highly asymmetric magnetic field density, whereinthe electric field and the electric field density, and the magneticfield and the magnetic field density, are more concentrated away fromthe base interior surface.

Example 2—Transverse Magnetic Wave Frequency of a Conical CavityResonator

In some embodiments, a frequency of a hollow conical cavity resonator iscalculated per the equations below:

For an azimuthal eigenvalue (m) of the resonator:

m=n where n=0,1,2, . . .

For a polar eigenvalue (l), an azimuthal eigenvalue (m), a taper angle(θ₀), and a polar wave equation (P_(l) ^(m)(cos θ)) of the resonator:

[P _(l) ^(m)(cos θ)]_(θ=θ) ₀ =0

For a radial eigenvalue (k), a polar eigenvalue (l), a radial length(r₁), and a radial wave equation (j_(l)(kr)) of the resonator:

$\left\lbrack {\frac{d}{dr}\left\lbrack {({kr}){j_{l}({kr})}} \right\rbrack} \right\rbrack_{r = 0} = {{0\mspace{14mu} {{and}\mspace{14mu}\left\lbrack {\frac{d}{dr}\left\lbrack {({kr}){j_{l}({kr})}} \right\rbrack} \right\rbrack}_{r = r_{1}}} = 0}$

For a radial eigenvalue (k), a polar eigenvalue (l), a radial length(r₁), and a radial wave equation (j_(l)(kr)) of the resonator:

[(kr)j _(l)(kr)]_(r=0)=0 or [(kr)j _(l)(kr)]_(r=r) ₁ =0

For a frequency (f), a radial eigenvalue (k), and a speed of light (c)of the resonator:

$f = \frac{kc}{2\pi}$

FIGS. 22 and 23 are non-limiting exemplary plots of a first and a secondazimuthal eigenfunction of a conical cavity resonator, respectively.FIGS. 24 and 25 are non-limiting exemplary plots of a first and a secondtransverse magnetic polar eigenfunction of a conical cavity resonator,respectively. FIGS. 26 and 27 are non-limiting exemplary plots of afirst and a second transverse magnetic radial eigenfunction of a conicalcavity resonator, respectively. FIGS. 28 and 29 are non-limitingexemplary plots of a first and a second transverse magnetic evanescentradial eigenfunction of a conical cavity resonator, respectively.

FIG. 50 is an exemplary perspective view of a first transverse magneticthree-dimensional electric field vector plot of a non-limiting conicalcavity resonator. FIG. 51 is an exemplary perspective view of a firsttransverse magnetic three-dimensional magnetic field vector plot of anon-limiting conical cavity resonator.

FIG. 52 is an exemplary axial cross section view of a first electricfield transverse magnetic density plot of a non-limiting conical cavityresonator. FIG. 53 is an exemplary axial cross section view of a firstmagnetic field transverse magnetic vector plot of a non-limiting conicalcavity resonator.

FIG. 54 is an exemplary radial cross section view of a first electricfield transverse magnetic vector plot of a non-limiting conical cavityresonator. FIG. 55 is an exemplary radial cross section view of a firstelectric field transverse magnetic vector plot of a non-limiting conicalcavity resonator comprising a substantially flat base interior surface.

FIG. 56 is an exemplary radial cross section view of a first magneticfield transverse magnetic density plot of a non-limiting conical cavityresonator. FIG. 57 is an exemplary radial cross section view of a firstmagnetic field transverse magnetic density plot of a non-limitingconical cavity resonator comprising a substantially flat base interiorsurface.

FIG. 62 is an exemplary perspective view of a second transverse magneticthree-dimensional electric field vector plot of a non-limiting conicalcavity resonator. FIG. 63 is an exemplary perspective view of a secondtransverse magnetic three-dimensional magnetic field vector plot of anon-limiting conical cavity resonator.

FIG. 64 is an exemplary axial cross section view of a second electricfield transverse magnetic density plot of a non-limiting conical cavityresonator. FIG. 65 is an exemplary axial cross section view of a secondmagnetic field transverse magnetic vector plot of a non-limiting conicalcavity resonator.

FIG. 66 is an exemplary radial cross section view of a second electricfield transverse magnetic vector plot of a non-limiting conical cavityresonator. FIG. 67 is an exemplary radial cross section view of a secondelectric field transverse magnetic vector plot of a non-limiting conicalcavity resonator comprising a substantially flat base interior surface.

FIG. 68 is an exemplary radial cross section view of a second magneticfield transverse magnetic density plot of a non-limiting conical cavityresonator. FIG. 69 is an exemplary radial cross section view of a secondmagnetic field transverse magnetic density plot of a non-limitingconical cavity resonator comprising a substantially flat base interiorsurface.

As the size of the arrows in the above figures are positively correlatedwith an electric field and an electric field density, or with a magneticfield and a magnetic field density, the non-limiting conical cavityresonator exhibits one or both a highly asymmetric electric field and ahighly asymmetric electric field density, and a highly asymmetricmagnetic field and a highly asymmetric magnetic field density, whereinthe electric field and the electric field density, and the magneticfield and the magnetic field density, are more concentrated away fromthe tapered interior surface.

Example 3—Transverse Electric Wave Frequency of a Truncated ConicalCavity Resonator

In some embodiments, a frequency of a hollow conical cavity resonator iscalculated per the equations below:

For an azimuthal eigenvalue (m) of the resonator:

m=n where n=0,1,2, . . .

For a polar eigenvalue (l), an azimuthal eigenvalue (m), a taper angle(θ₀), and a polar wave equation (P_(l) ^(m)(cos θ)) of the resonator:

$\left\lbrack {\frac{d}{d\; \theta}\left\lbrack {P_{l}^{m}\left( {\cos \mspace{11mu} \theta} \right)} \right\rbrack} \right\rbrack_{\theta = \theta_{0}} = 0$

For a radial eigenvalue (k), a polar eigenvalue (l), a truncated radiallength (r₀), a radial length (r₁), and a radial wave equation(h_(l)(kr)) of the resonator:

[(kr)h _(l)(kr)]_(r=r) ₀ =0 and [(kr)h _(l)(kr)]_(r=r) ₁ =0

For a radial eigenvalue (k), a polar eigenvalue (l), a radial length(r₁), a truncated radial length (r₀), and a radial wave equation(h_(l)(kr)) of the resonator:

$\left\lbrack {\frac{d}{dr}\left\lbrack {({kr}){h_{l}({kr})}} \right\rbrack} \right\rbrack_{r = 0} = {{0\mspace{14mu} {{or}\mspace{14mu}\left\lbrack {\frac{d}{dr}\left\lbrack {({kr}){h_{l}({kr})}} \right\rbrack} \right\rbrack}_{r = r_{1}}} = 0}$

For a frequency (f), a radial eigenvalue (k), and a speed of light (c)of the resonator:

$f = \frac{kc}{2\pi}$

FIGS. 22 and 23 are non-limiting exemplary plots of a first and a secondazimuthal eigenfunction of a conical cavity resonator, respectively.FIGS. 30 and 31 are non-limiting exemplary plots of a first and a secondtransverse electric polar eigenfunction of a conical cavity resonator,respectively. FIGS. 32 and 33 are non-limiting exemplary plots of afirst and a second transverse electric radial eigenfunction of a conicalcavity resonator, respectively. FIGS. 34 and 35 are non-limitingexemplary plots of a first and a second transverse electric evanescentradial eigenfunction of a conical cavity resonator, respectively.

FIG. 74 is an exemplary perspective view of a first transverse electricthree-dimensional electric field vector plot of a non-limiting conicalcavity resonator. FIG. 75 is an exemplary perspective view of a firsttransverse electric three-dimensional magnetic field vector plot of anon-limiting conical cavity resonator.

FIG. 76 is an exemplary axial cross section view of a first electricfield transverse electric vector plot of a non-limiting conical cavityresonator. FIG. 77 is an exemplary axial cross section view of a firstmagnetic field transverse electric vector plot of a non-limiting conicalcavity resonator.

FIG. 82 is an exemplary radial cross section view of a first electricfield transverse electric vector plot of a non-limiting truncatedconical cavity resonator. FIG. 83 is an exemplary radial cross sectionview of a first electric field transverse electric vector plot of anon-limiting truncated conical cavity resonator comprising asubstantially flat base and truncated interior surfaces.

FIG. 84 is an exemplary radial cross section view of a first magneticfield transverse electric vector plot of a non-limiting truncatedconical cavity resonator. FIG. 85 is an exemplary radial cross sectionview of a first magnetic field transverse electric vector plot of anon-limiting truncated conical cavity resonator comprising asubstantially flat base and truncated interior surfaces.

As the size of the arrows in the above figures are positively correlatedwith an electric field and an electric field density, or with a magneticfield and a magnetic field density, the non-limiting conical cavityresonator exhibits one or both a highly asymmetric electric field and ahighly asymmetric electric field density, and a highly asymmetricmagnetic field and a highly asymmetric magnetic field density, whereinthe electric field and the electric field density, and the magneticfield and the magnetic field density, are more concentrated away fromthe base interior surface.

Example 4—Transverse Magnetic Wave Frequency of a Truncated ConicalCavity Resonator

In some embodiments, a frequency of a hollow conical cavity resonator iscalculated per the equations below:

For an azimuthal eigenvalue (m) of the resonator:

m=n where n=0,1,2, . . .

For a polar eigenvalue (l), an azimuthal eigenvalue (m), a taper angle(θ₀), and a polar wave equation (P_(l) ^(m)(cos θ)) of the resonator:

[P _(l) ^(m)(cos θ)]_(θ=θ) ₀ =0

For a radial eigenvalue (k), a polar eigenvalue (l), a truncated radiallength (r₀), a radial length (r₁), and a radial wave equation(h_(l)(kr)) of the resonator:

$\left\lbrack {\frac{d}{dr}\left\lbrack {({kr}){h_{l}({kr})}} \right\rbrack} \right\rbrack_{r = 0} = {0\mspace{14mu} {{and}\mspace{14mu}\left\lbrack {\frac{d}{dr}\left\lbrack {({kr}){h_{l}({kr})}} \right\rbrack} \right\rbrack}_{r = r_{1}}}$

For a radial eigenvalue (k), a polar eigenvalue (l), a truncated radiallength (r₀), a radial length (r₁), and a radial wave equation(h_(l)(kr)) of the resonator:

[(kr)h _(l)(kr)]_(r=r) ₀ =0 or [(kr)h _(l)(kr)]_(r=r) ₁ =0

For a frequency (f), a radial eigenvalue (k), and a speed of light (c)of the resonator:

$f = \frac{kc}{2\pi}$

FIGS. 22 and 23 are non-limiting exemplary plots of a first and a secondazimuthal eigenfunction of a conical cavity resonator, respectively.FIGS. 24 and 25 are non-limiting exemplary plots of a first and a secondtransverse magnetic polar eigenfunction of a conical cavity resonator,respectively. FIGS. 26 and 27 are non-limiting exemplary plots of afirst and a second transverse magnetic radial eigenfunction of a conicalcavity resonator, respectively. FIGS. 28 and 29 are non-limitingexemplary plots of a first and a second transverse magnetic evanescentradial eigenfunction of a conical cavity resonator, respectively.

FIG. 50 is an exemplary perspective view of a first transverse magneticthree-dimensional electric field vector plot of a non-limiting conicalcavity resonator. FIG. 51 is an exemplary perspective view of a firsttransverse magnetic three-dimensional magnetic field vector plot of anon-limiting conical cavity resonator.

FIG. 52 is an exemplary axial cross section view of a first electricfield transverse magnetic density plot of a non-limiting conical cavityresonator. FIG. 53 is an exemplary axial cross section view of a firstmagnetic field transverse magnetic vector plot of a non-limiting conicalcavity resonator.

FIG. 58 is an exemplary radial cross section view of a first electricfield transverse magnetic vector plot of a non-limiting truncatedconical cavity resonator. FIG. 59 is an exemplary radial cross sectionview of a first electric field transverse magnetic vector plot of anon-limiting truncated conical cavity resonator comprising asubstantially flat base and truncated interior surfaces.

FIG. 60 is an exemplary radial cross section view of a first magneticfield transverse magnetic density plot of a non-limiting truncatedconical cavity resonator. FIG. 61 is an exemplary radial cross sectionview of a first magnetic field transverse magnetic density plot of anon-limiting truncated conical cavity resonator comprising asubstantially flat base and truncated interior surfaces.

FIG. 62 is an exemplary perspective view of a second transverse magneticthree-dimensional electric field vector plot of a non-limiting conicalcavity resonator. FIG. 63 is an exemplary perspective view of a secondtransverse magnetic three-dimensional magnetic field vector plot of anon-limiting conical cavity resonator.

FIG. 64 is an exemplary axial cross section view of a second electricfield transverse magnetic density plot of a non-limiting conical cavityresonator. FIG. 65 is an exemplary axial cross section view of a secondmagnetic field transverse magnetic vector plot of a non-limiting conicalcavity resonator.

FIG. 70 is an exemplary radial cross section view of a second electricfield transverse magnetic vector plot of a non-limiting truncatedconical cavity resonator. FIG. 71 is an exemplary radial cross sectionview of a second electric field transverse magnetic vector plot of anon-limiting truncated conical cavity resonator comprising asubstantially flat base and truncated interior surfaces.

FIG. 72 is an exemplary radial cross section view of a second magneticfield transverse magnetic density plot of a non-limiting truncatedconical cavity resonator. FIG. 73 is an exemplary radial cross sectionview of a second magnetic field transverse magnetic density plot of anon-limiting truncated conical cavity resonator comprising asubstantially flat base and truncated interior surfaces.

As the size of the arrows in the above figures are positively correlatedwith an electric field and an electric field density, or with a magneticfield and a magnetic field density, the non-limiting conical cavityresonator exhibits one or both a highly asymmetric electric field and ahighly asymmetric electric field density, and a highly asymmetricmagnetic field and a highly asymmetric magnetic field density, whereinthe electric field and the electric field density, and the magneticfield and the magnetic field density, are more concentrated away fromone or both the tapered interior surface and the truncated interiorsurface.

Example 5—Transverse Electric Wave Frequency of a Pyramidal CavityResonator

In some embodiments, a frequency of a hollow pyramidal cavity resonatoris calculated per the equations below:

For an azimuthal eigenvalue (m) and a taper angle (φ₀) of the resonator:

${m = {{\frac{n\; \pi}{\phi_{0}}\mspace{14mu} {where}\mspace{14mu} n} = 0}},1,2,\ldots$

For a polar eigenvalue (l), an azimuthal eigenvalue (m), a taper angle(θ₀), a polar wave equation (P_(l) ^(m)(cos θ)), and a polar waveequation (Q_(l) ^(m)(cos θ)) of the resonator:

$\left\lbrack {\frac{d}{d\; \theta}\left\lbrack {{{P_{l}^{m}\left( {\cos \frac{\theta_{0}}{2}} \right)}{Q_{l}^{m}\left( {{- \cos}\frac{\theta_{0}}{2}} \right)}} - {{P_{l}^{m}\left( {{- \cos}\frac{\theta_{0}}{2}} \right)}{Q_{l}^{m}\left( {\cos \frac{\theta_{0}}{2}} \right)}}} \right\rbrack} \right\rbrack_{\theta = \theta_{0}} = 0$

For a radial eigenvalue (k), a polar eigenvalue (l), a radial length(r₁), and a radial wave equation (j_(l)(kr)) of the resonator:

[(kr)j _(l)(kr)]_(r=0)=0 and [(kr)j _(l)(kr)]_(r=r) ₁ =0

For a radial eigenvalue (k), a polar eigenvalue (l), a radial length(r₁), and a radial wave equation (j_(l)(kr)) of the resonator:

$\left\lbrack {\frac{d}{dr}\left\lbrack {({kr}){j_{l}({kr})}} \right\rbrack} \right\rbrack_{r = 0} = {{0\mspace{14mu} {{or}\mspace{14mu}\left\lbrack {\frac{d}{dr}\left\lbrack {({kr}){j_{l}({kr})}} \right\rbrack} \right\rbrack}_{r = r_{1}}} = 0}$

For a frequency (f), a radial eigenvalue (k), and a speed of light (c)of the resonator:

$f = \frac{kc}{2\pi}$

FIGS. 36 and 37 are non-limiting exemplary plots of a first and a secondazimuthal eigenfunction of a pyramidal cavity resonator, respectively.FIGS. 44 and 45 are non-limiting exemplary plots of a first and a secondtransverse electric polar eigenfunction of a pyramidal cavity resonator,respectively. FIGS. 46 and 47 are non-limiting exemplary plots of afirst and a second transverse electric radial eigenfunction of apyramidal cavity resonator, respectively. FIGS. 48 and 49 arenon-limiting exemplary plots of a first and a second transverse electricevanescent radial eigenfunction of a pyramidal cavity resonator,respectively.

FIG. 110 is an exemplary perspective view of a first transverse electricthree-dimensional electric field vector plot of a non-limiting pyramidalcavity resonator. FIG. 111 is an exemplary perspective view of a firsttransverse electric three-dimensional magnetic field vector plot of anon-limiting pyramidal cavity resonator.

FIG. 112 is an exemplary axial cross section view of a first electricfield transverse electric density plot of a non-limiting pyramidalcavity resonator. FIG. 113 is an exemplary axial cross section view of afirst magnetic field transverse electric vector plot of a non-limitingpyramidal cavity resonator.

FIG. 114 is an exemplary radial cross section view of a first electricfield transverse electric vector plot of a non-limiting pyramidal cavityresonator. FIG. 115 is an exemplary radial cross section view of a firstelectric field transverse electric vector plot of a non-limitingpyramidal resonator comprising a substantially flat base interiorsurface.

FIG. 116 is an exemplary radial cross section view of a first magneticfield transverse electric vector plot of a non-limiting pyramidal cavityresonator. FIG. 117 is an exemplary radial cross section view of a firstmagnetic field transverse electric vector plot of a non-limitingpyramidal cavity resonator comprising a substantially flat base interiorsurface.

As the size of the arrows in the above figures are positively correlatedwith an electric field and an electric field density, or with a magneticfield and a magnetic field density, the non-limiting pyramidal cavityresonator exhibits one or both a highly asymmetric electric field and ahighly asymmetric electric field density, and a highly asymmetricmagnetic field and a highly asymmetric magnetic field density, whereinthe electric field and the electric field density, and the magneticfield and the magnetic field density, are more concentrated away fromthe base interior surface.

Example 6—Transverse Magnetic Wave Frequency of a Pyramidal CavityResonator

In some embodiments, a frequency of a hollow pyramidal cavity resonatoris calculated per the equations below:

For an azimuthal eigenvalue (m) and a taper angle (φ₀) of the resonator:

${{m = {{\frac{n\; \pi}{\phi_{0}}\mspace{14mu} {where}\mspace{20mu} n} = 0}},1,2,\ldots}\;$

For a polar eigenvalue (l), an azimuthal eigenvalue (m), a taper angle(θ₀), a polar wave equation (P_(l) ^(m)(cos θ)), and a polar waveequation (Q_(l) ^(m)(cos θ)) of the resonator:

$\left\lbrack {{{P_{l}^{m}\left( {\cos \frac{\theta_{0}}{2}} \right)}{Q_{l}^{m}\left( {{- \cos}\frac{\theta_{0}}{2}} \right)}} - {{P_{l}^{m}\left( {{- \cos}\frac{\theta_{0}}{2}} \right)}{Q_{l}^{m}\left( {\cos \frac{\theta_{0}}{2}} \right)}}} \right\rbrack_{\theta = \theta_{0}} = 0$

For a radial eigenvalue (k), a polar eigenvalue (l), a radial length(r₁), and a radial wave equation (j_(l)(kr)) of the resonator:

$\left\lbrack {\frac{d}{dr}\left\lbrack {({kr}){j_{l}({kr})}} \right\rbrack} \right\rbrack_{r = 0} = {{0\mspace{14mu} {{and}\mspace{14mu}\left\lbrack {\frac{d}{dr}\left\lbrack {({kr}){j_{l}({kr})}} \right\rbrack} \right\rbrack}_{r = r_{1}}} = 0}$

For a radial eigenvalue (k), a polar eigenvalue (l), a radial length(r₁), and a radial wave equation (j_(l)(kr)) of the resonator:

[(kr)j _(l)(kr)]_(r=0)=0 or [(kr)j _(l)(kr)]_(r=r) ₁ =0

For a frequency (f), a radial eigenvalue (k), and a speed of light (c)of the resonator:

$f = \frac{kc}{2\pi}$

FIGS. 36 and 37 are non-limiting exemplary plots of a first and a secondazimuthal eigenfunction of a pyramidal cavity resonator, respectively.FIGS. 38 and 39 are non-limiting exemplary plots of a first and a secondtransverse magnetic polar eigenfunction of a pyramidal cavity resonator,respectively. FIGS. 40 and 41 are non-limiting exemplary plots of afirst and a second transverse magnetic radial eigenfunction of apyramidal cavity resonator, respectively. FIGS. 42 and 43 arenon-limiting exemplary plots of a first and a second transverse magneticevanescent radial eigenfunction of a pyramidal cavity resonator,respectively.

FIG. 86 is an exemplary perspective view of a first transverse magneticthree-dimensional electric field vector plot of a non-limiting pyramidalcavity resonator. FIG. 87 is an exemplary perspective view of a firsttransverse magnetic three-dimensional magnetic field vector plot of anon-limiting pyramidal cavity resonator.

FIG. 88 is an exemplary axial cross section view of a first electricfield transverse magnetic density plot of a non-limiting pyramidalcavity resonator. FIG. 89 is an exemplary axial cross section view of afirst magnetic field transverse magnetic vector plot of a non-limitingpyramidal cavity resonator.

FIG. 90 is an exemplary radial cross section view of a first electricfield transverse magnetic vector plot of a non-limiting pyramidal cavityresonator. FIG. 91 is an exemplary radial cross section view of a firstelectric field transverse magnetic vector plot of a non-limitingpyramidal cavity resonator comprising a substantially flat base interiorsurface.

FIG. 92 is an exemplary radial cross section view of a first magneticfield transverse magnetic density plot of a non-limiting pyramidalcavity resonator. FIG. 93 is an exemplary radial cross section view of afirst magnetic field transverse magnetic density plot of a non-limitingpyramidal cavity resonator comprising a substantially flat base interiorsurface.

FIG. 98 is an exemplary perspective view of a second transverse magneticthree-dimensional electric field vector plot of a non-limiting pyramidalcavity resonator. FIG. 99 is an exemplary perspective view of a secondtransverse magnetic three-dimensional magnetic field vector plot of anon-limiting pyramidal cavity resonator.

FIG. 100 is an exemplary axial cross section view of a second electricfield transverse magnetic density plot of a non-limiting pyramidalcavity resonator. FIG. 101 is an exemplary axial cross section view of asecond magnetic field transverse magnetic vector plot of a non-limitingpyramidal cavity resonator.

FIG. 102 is an exemplary radial cross section view of a second electricfield transverse magnetic vector plot of a non-limiting pyramidal cavityresonator. FIG. 103 is an exemplary radial cross section view of asecond electric field transverse magnetic vector plot of a non-limitingpyramidal cavity resonator comprising a substantially flat base interiorsurface.

FIG. 104 is an exemplary radial cross section view of a second magneticfield transverse magnetic density plot of a non-limiting pyramidalcavity resonator. FIG. 105 is an exemplary radial cross section view ofa second magnetic field transverse magnetic density plot of anon-limiting pyramidal cavity resonator comprising a substantially flatbase interior surface.

As the size of the arrows in the above figures are positively correlatedwith an electric field and an electric field density, or with a magneticfield and a magnetic field density, the non-limiting pyramidal cavityresonator exhibits one or both a highly asymmetric electric field and ahighly asymmetric electric field density, and a highly asymmetricmagnetic field and a highly asymmetric magnetic field density, whereinthe electric field and the electric field density, and the magneticfield and the magnetic field density, are more concentrated away fromone or more of the at least three tapered interior surfaces.

Example 7—Transverse Electric Wave Frequency of a Truncated PyramidalCavity Resonator

In some embodiments, a frequency of a hollow pyramidal cavity resonatoris calculated per the equations below:

For an azimuthal eigenvalue (m) and a taper angle (φ₀) of the resonator:

${m = {{\frac{n\; \pi}{\phi_{0}}\mspace{20mu} {where}\mspace{14mu} n} = 0}},1,2,\ldots$

For a polar eigenvalue (l), an azimuthal eigenvalue (m), a taper angle(θ₀), a polar wave equation (P_(l) ^(m)(cos θ)), and a polar waveequation (Q_(l) ^(m)(cos θ)) of the resonator:

$\left\lbrack {\frac{d}{d\; \theta}\left\lbrack {{{P_{l}^{m}\left( {\cos \frac{\theta_{0}}{2}} \right)}{Q_{l}^{m}\left( {{- \cos}\frac{\theta_{0}}{2}} \right)}} - {{P_{l}^{m}\left( {{- \cos}\frac{\theta_{0}}{2}} \right)}{Q_{l}^{m}\left( {\cos \frac{\theta_{0}}{2}} \right)}}} \right\rbrack} \right\rbrack_{\theta = \theta_{0}} = 0$

For a radial eigenvalue (k), a polar eigenvalue (l), a truncated radiallength (r₀), a radial length (r₁), and a radial wave equation(h_(l)(kr)) of the resonator:

[(kr)h _(l)(kr)]_(r=r) ₀ =0 and [(kr)h _(l)(kr)]_(r=r) ₁ =0

For a radial eigenvalue (k), a polar eigenvalue (l), a radial length(r₁), a truncated radial length (r₀), and a radial wave equation(h_(l)(kr)) of the resonator:

$\left\lbrack {\frac{d}{dr}\left\lbrack {({kr}){h_{l}({kr})}} \right\rbrack} \right\rbrack_{r = r_{0}} = {0\mspace{14mu} {{or}\mspace{14mu}\left\lbrack {\frac{d}{dr}\left\lbrack {({kr}){h_{l}({kr})}} \right\rbrack} \right\rbrack}_{r = r_{1}}}$

For a frequency (f), a radial eigenvalue (k), and a speed of light (c)of the resonator:

$f = \frac{kc}{2\pi}$

FIGS. 36 and 37 are non-limiting exemplary plots of a first and a secondazimuthal eigenfunction of a pyramidal cavity resonator, respectively.FIGS. 44 and 45 are non-limiting exemplary plots of a first and a secondtransverse electric polar eigenfunction of a pyramidal cavity resonator,respectively. FIGS. 46 and 47 are non-limiting exemplary plots of afirst and a second transverse electric radial eigenfunction of apyramidal cavity resonator, respectively. FIGS. 48 and 49 arenon-limiting exemplary plots of a first and a second transverse electricevanescent radial eigenfunction of a pyramidal cavity resonator,respectively.

FIG. 110 is an exemplary perspective view of a first transverse electricthree-dimensional electric field vector plot of a non-limiting pyramidalcavity resonator. FIG. 111 is an exemplary perspective view of a firsttransverse electric three-dimensional magnetic field vector plot of anon-limiting pyramidal cavity resonator.

FIG. 112 is an exemplary axial cross section view of a first electricfield transverse electric density plot of a non-limiting pyramidalcavity resonator. FIG. 113 is an exemplary axial cross section view of afirst magnetic field transverse electric vector plot of a non-limitingpyramidal cavity resonator.

FIG. 118 is an exemplary radial cross section view of a first electricfield transverse electric vector plot of a non-limiting truncatedpyramidal cavity resonator. FIG. 119 is an exemplary radial crosssection view of a first electric field transverse electric vector plotof a non-limiting truncated pyramidal resonator comprising asubstantially flat base and truncated interior surfaces.

FIG. 120 is an exemplary radial cross section view of a first magneticfield transverse electric vector plot of a non-limiting truncatedpyramidal cavity resonator. FIG. 121 is an exemplary radial crosssection view of a first magnetic field transverse electric vector plotof a non-limiting truncated pyramidal cavity resonator comprising asubstantially flat base and truncated interior surfaces.

As the size of the arrows in the above figures are positively correlatedwith an electric field and an electric field density, or with a magneticfield and a magnetic field density, the non-limiting pyramidal cavityresonator exhibits one or both a highly asymmetric electric field and ahighly asymmetric electric field density, and a highly asymmetricmagnetic field and a highly asymmetric magnetic field density, whereinthe electric field and the electric field density, and the magneticfield and the magnetic field density, are more concentrated away fromthe base interior surface.

Example 8—Transverse Magnetic Wave Frequency of a Truncated PyramidalCavity Resonator

In some embodiments, a frequency of a hollow pyramidal cavity resonatoris calculated per the equations below:

For an azimuthal eigenvalue (m) and a taper angle (φ₀) of the resonator:

${m = {{\frac{n\; \pi}{\phi_{0}}\mspace{20mu} {where}\mspace{14mu} n} = 0}},1,2,\ldots$

For a polar eigenvalue (l), an azimuthal eigenvalue (m), a taper angle(θ₀), a polar wave equation (P_(l) ^(m)(cos θ)), and a polar waveequation (Q_(l) ^(m)(cos θ)) of the resonator:

$\left\lbrack {{{P_{l}^{m}\left( {\cos \frac{\theta_{0}}{2}} \right)}{Q_{l}^{m}\left( {{- \cos}\frac{\theta_{0}}{2}} \right)}} - {{P_{l}^{m}\left( {{- \cos}\frac{\theta_{0}}{2}} \right)}{Q_{l}^{m}\left( {\cos \frac{\theta_{0}}{2}} \right)}}} \right\rbrack_{\theta = \theta_{0}} = 0$

For a radial eigenvalue (k), a polar eigenvalue (l), a truncated radiallength (r₀), a radial length (r₁), and a radial wave equation(h_(l)(kr)) of the resonator:

$\left\lbrack {\frac{d}{dr}\left\lbrack {({kr}){h_{l}({kr})}} \right\rbrack} \right\rbrack_{r = r_{0}} = {{0\mspace{14mu} {{and}\mspace{14mu}\left\lbrack {\frac{d}{dr}\left\lbrack {({kr}){h_{l}({kr})}} \right\rbrack} \right\rbrack}_{r = r_{1}}} = 0}$

For a radial eigenvalue (k), a polar eigenvalue (l), a truncated radiallength (r₀), a radial length (r₁), and a radial wave equation(h_(l)(kr)) of the resonator:

[(kr)h _(l)(kr)]_(r=r) ₀ =0 or [(kr)h _(l)(kr)]_(r=r) ₁ =0

For a frequency (f), a radial eigenvalue (k), and a speed of light (c)of the resonator:

$f = \frac{kc}{2\pi}$

FIGS. 36 and 37 are non-limiting exemplary plots of a first and a secondazimuthal eigenfunction of a pyramidal cavity resonator, respectively.FIGS. 38 and 39 are non-limiting exemplary plots of a first and a secondtransverse magnetic polar eigenfunction of a pyramidal cavity resonator,respectively. FIGS. 40 and 41 are non-limiting exemplary plots of afirst and a second transverse magnetic radial eigenfunction of apyramidal cavity resonator, respectively. FIGS. 42 and 43 arenon-limiting exemplary plots of a first and a second transverse magneticevanescent radial eigenfunction of a pyramidal cavity resonator,respectively.

FIG. 86 is an exemplary perspective view of a first transverse magneticthree-dimensional electric field vector plot of a non-limiting pyramidalcavity resonator. FIG. 87 is an exemplary perspective view of a firsttransverse magnetic three-dimensional magnetic field vector plot of anon-limiting pyramidal cavity resonator.

FIG. 88 is an exemplary axial cross section view of a first electricfield transverse magnetic density plot of a non-limiting pyramidalcavity resonator. FIG. 89 is an exemplary axial cross section view of afirst magnetic field transverse magnetic vector plot of a non-limitingpyramidal cavity resonator.

FIG. 94 is an exemplary radial cross section view of a first electricfield transverse magnetic vector plot of a non-limiting truncatedpyramidal cavity resonator. FIG. 95 is an exemplary radial cross sectionview of a first electric field transverse magnetic vector plot of anon-limiting truncated pyramidal cavity resonator comprising asubstantially flat base and truncated interior surfaces.

FIG. 96 is an exemplary radial cross section view of a first magneticfield transverse magnetic density plot of a non-limiting truncatedpyramidal cavity resonator. FIG. 97 is an exemplary radial cross sectionview of a first magnetic field transverse magnetic density plot of anon-limiting truncated pyramidal cavity resonator comprising asubstantially flat base and truncated interior surfaces.

FIG. 98 is an exemplary perspective view of a second transverse magneticthree-dimensional electric field vector plot of a non-limiting pyramidalcavity resonator. FIG. 99 is an exemplary perspective view of a secondtransverse magnetic three-dimensional magnetic field vector plot of anon-limiting pyramidal cavity resonator.

FIG. 100 is an exemplary axial cross section view of a second electricfield transverse magnetic density plot of a non-limiting pyramidalcavity resonator. FIG. 101 is an exemplary axial cross section view of asecond magnetic field transverse magnetic vector plot of a non-limitingpyramidal cavity resonator.

FIG. 106 is an exemplary radial cross section view of a second electricfield transverse magnetic vector plot of a non-limiting truncatedpyramidal cavity resonator. FIG. 107 is an exemplary radial crosssection view of a second electric field transverse magnetic vector plotof a non-limiting truncated pyramidal cavity resonator comprising asubstantially flat base and truncated interior surfaces.

FIG. 108 is an exemplary radial cross section view of a second magneticfield transverse magnetic density plot of a non-limiting truncatedpyramidal cavity resonator. FIG. 109 is an exemplary radial crosssection view of a second magnetic field transverse magnetic density plotof a non-limiting truncated pyramidal cavity resonator comprising asubstantially flat base and truncated interior surfaces.

As the size of the arrows in the above figures are positively correlatedwith an electric field and an electric field density, or with a magneticfield and a magnetic field density, the non-limiting pyramidal cavityresonator exhibits one or both a highly asymmetric electric field and ahighly asymmetric electric field density, and a highly asymmetricmagnetic field and a highly asymmetric magnetic field density, whereinthe electric field and the electric field density, and the magneticfield and the magnetic field density, are more concentrated away fromone or more of the at least three tapered interior surfaces and thetruncated interior surface.

Terms and Definitions

Unless otherwise defined, all technical terms used herein have the samemeaning as commonly understood by one of ordinary skill in the art towhich this disclosure belongs.

As used herein, the singular forms “a,” “an,” and “the” include pluralreferences unless the context clearly dictates otherwise.

As used herein, the term “about” refers to an amount that is near thestated amount by about 10%, 5%, or 1%, including increments therein.

The embodiments of the invention described above are intended to bemerely exemplary; numerous variations and modifications will be apparentto those skilled in the art. Such variations and modifications areintended to be within the scope of the present invention as defined byany of the appended claims.

What is claimed is:
 1. An electromagnetic energy momentum thrustercomprising: a) a cavity resonator forming a cavity having a baseinterior surface and a tapered interior surface, the tapered interiorsurface converging to an apex point; and b) an electromagnetic radiationsource in communication with the cavity resonator, the electromagneticradiation source configured to emit an electromagnetic wave having afrequency between about 1.0 MHz to about 1000 THz into the cavityresonator.
 2. The thruster of claim 1, wherein the electromagneticradiation source is configured to produce the frequency of theelectromagnetic wave in evanescence so that the electromagnetic wave hasa maximum field amplitude and an asymptotic field amplitude, the maximumfield amplitude being at, or adjacent to, the base interior surface, theasymptotic field amplitude being at, or adjacent to, one or both thetapered interior surface and the apex point.
 3. The thruster of claim 1,wherein the electromagnetic radiation source is configured to producethe frequency of the electromagnetic wave in evanescence so that theelectromagnetic wave has a maximum field amplitude and an asymptoticfield amplitude, the maximum field amplitude being at, or adjacent to,one or both the tapered interior surface and the apex point, and theasymptotic field amplitude being at, or adjacent to, the base interiorsurface.
 4. The thruster of claim 1, wherein the cavity includes anoverall interior surface that includes the base and tapered interiorsurfaces, substantially the entire overall interior surface beingelectrically conductive, wherein the cavity resonator has a qualityfactor between about 10{circumflex over ( )}3 to about 10{circumflexover ( )}9.
 5. The thruster of claim 1, wherein the cavity includes anoverall interior surface that includes the base and tapered interiorsurfaces, the overall interior surface comprises aluminum, antimony,arsenic, barium, beryllium, bismuth, cadmium, calcium, carbon, chromium,cobalt, copper, gallium, gold, hydrogen, indium, iron, lanthanum, lead,lithium, magnesium, manganese, mercury, molybdenum, nickel, niobium,nitrogen, oxygen, palladium, phosphorus, platinum, scandium, silicon,silver, strontium, sulfur, tantalum, technetium, tin, titanium,tungsten, vanadium, yttrium, zinc, zirconium, or any combinationthereof.
 6. The thruster of claim 1, wherein the cavity includes anoverall interior surface that includes the base and tapered interiorsurfaces, substantially the entire overall interior surface beingsuperconductive, wherein the cavity resonator has a quality factorbetween about 10{circumflex over ( )}6 to about 10{circumflex over( )}15.
 7. The thruster of claim 1, wherein the cavity includes anoverall interior surface that includes the base and tapered interiorsurfaces, the overall interior surface comprises aluminum, barium,beryllium, bismuth, cadmium, calcium, copper, gallium, gadolinium,germanium, lanthanum, lead, lithium, indium, mercury, molybdenum,niobium, nitrogen, osmium, oxygen, protactinium, rhenium, ruthenium,silicon, strontium, sulfur, tantalum, technetium, thallium, thorium,titanium, tin, vanadium, yttrium, zinc, zirconium, NbTi, PbMoS, V₃Ga,NbN, V₃Si, Nb₃Sn, Nb₃Al, Nb₃(AlGe), Nb₃Ge, Bi₂Sr₂CuO₆, Bi₂Sr₂CaCu₂O₈,Bi₂Sr₂Ca₂Cu₃O₁₀, YBa₂Cu₃O₇, YBa₂Cu₄O₈, Y₂Ba₄Cu₇O₁₅, Y₃Ba₅Cu₈O₁₈,Tl₂Ba₂CuO₆, Tl₂Ba₂CaCu₂O₈, Tl₂Ba₂Ca₂Cu₃O₁₀, TlBa₂Ca₃Cu₄O₁₁, HgBa₂CuO₄,HgBa₂CaCu₂O₆, HgBa₂Ca₂Cu₃O₈, or any combination thereof.
 8. The thrusterof claim 1, wherein the cavity comprises a vacuum with a pressurebetween about 10{circumflex over ( )}-24 Torr to about 10{circumflexover ( )}3 Torr.
 9. The thruster of claim 1, wherein the cavitycomprises a thermal reservoir with a temperature between about10{circumflex over ( )}-3 Kelvin to about 10{circumflex over ( )}3Kelvin.
 10. The thruster of claim 1, wherein the electromagnetic wavecomprises a transverse magnetic wave with a polar mode number of N1 andan azimuthal mode number of N2, where N1 and N2 are an integers from 0to 1000, and N1 is greater than or equal to N2.
 11. The thruster ofclaim 1, wherein the electromagnetic wave comprises a transversemagnetic wave with a polar mode number of N and an azimuthal mode numberof 0, where N is an integer from 0 to
 1000. 12. The thruster of claim 1,wherein the electromagnetic wave comprises a transverse magnetic wavewith a polar mode number of N and an azimuthal mode number of N, where Nis an integer from 0 to
 1000. 13. The thruster of claim 1, wherein theelectromagnetic wave comprises a transverse electric wave with a polarmode number of N1 and an azimuthal mode number of N2, where N1 and N2are an integers from 0 to 1000, and N1 is greater than or equal to N2.14. The thruster of claim 1, wherein the electromagnetic wave comprisesa transverse electric wave with a polar mode number of N and anazimuthal mode number of 0, where N is an integer from 0 to
 1000. 15.The thruster of claim 1, wherein the electromagnetic wave comprises atransverse electric wave with a polar mode number of N and an azimuthalmode number of N, where N is an integer from 0 to
 1000. 16. The thrusterof claim 1, wherein the electromagnetic radiation source is locatedinside the cavity at, or adjacent to, a maximum field amplitude or anasymptotic field amplitude of the electromagnetic wave.
 17. The thrusterof claim 1, wherein the cavity has at least one of a width and a heightbetween about 10{circumflex over ( )}-9 meters to about 10{circumflexover ( )}3 meters.
 18. The thruster of claim 1, wherein the taperedinterior surface forms an aperture angle between about 5 degrees toabout 175 degrees.
 19. The thruster of claim 1, wherein the cavity has awall with a wall thickness between about 10{circumflex over ( )}-9meters to about 1.0 meter.
 20. The thruster of claim 1, wherein the baseinterior surface is one or more of substantially elliptical,substantially circular, and substantially flat.
 21. The thruster ofclaim 1, wherein the electromagnetic wave forms an electromagneticenergy momentum tensor with an amplitude maximum at, or adjacent to, thebase interior surface, which results in one or more of a metric tensorcurvature, a thrust, and an acceleration of the thruster.
 22. Thethruster of claim 1, wherein the electromagnetic wave forms anelectromagnetic energy momentum tensor with an amplitude maximum at, oradjacent to, one or both the tapered interior surface and the apexpoint, which results in one or more of a metric tensor curvature, athrust, and an acceleration of the thruster.
 23. An electromagneticenergy momentum thruster comprising: a) a cavity resonator forming acavity having a base interior surface, a tapered interior surface, and atruncated interior surface opposing the base interior surface, thetapered interior surface being between the base and truncated interiorsurfaces; and b) an electromagnetic radiation source in communicationwith the cavity resonator, the electromagnetic radiation sourceconfigured to emit an electromagnetic wave having a frequency betweenabout 1.0 MHz to about 1000 THz into the cavity resonator, theelectromagnetic radiation source configured to produce theelectromagnetic wave in evanescence so that the electromagnetic wave hasa maximum field amplitude and an asymptotic field amplitude.
 24. Thethruster of claim 23, wherein the maximum field amplitude is at, oradjacent to, the base interior surface, and the asymptotic fieldamplitude is at, or adjacent to, one or both the tapered interiorsurface and the truncated interior surface.
 25. The thruster of claim23, wherein the maximum field amplitude is at, or adjacent to, one orboth the tapered interior surface and the truncated interior surface,and the asymptotic field amplitude is at, or adjacent to, the baseinterior surface.
 26. The thruster of claim 23, wherein the cavityincludes an overall interior surface that includes the base, tapered,and truncated interior surfaces, substantially the entire overallinterior surface being electrically conductive, wherein the cavityresonator has a quality factor between about 10{circumflex over ( )}3 toabout 10{circumflex over ( )}9.
 27. The thruster of claim 23, whereinthe cavity includes an overall interior surface that includes the base,tapered, and truncated interior surfaces, the overall interior surfacecomprises aluminum, antimony, arsenic, barium, beryllium, bismuth,cadmium, calcium, carbon, chromium, cobalt, copper, gallium, gold,hydrogen, indium, iron, lanthanum, lead, lithium, magnesium, manganese,mercury, molybdenum, nickel, niobium, nitrogen, oxygen, palladium,phosphorus, platinum, scandium, silicon, silver, strontium, sulfur,tantalum, technetium, tin, titanium, tungsten, vanadium, yttrium, zinc,zirconium, or any combination thereof.
 28. The thruster of claim 23,wherein the cavity includes an overall interior surface that includesthe base, tapered, and truncated interior surfaces, substantially theentire overall interior surface being superconductive, wherein thecavity resonator has a quality factor between about 10{circumflex over( )}6 to about 10{circumflex over ( )}15.
 29. The thruster of claim 23,wherein the cavity includes an overall interior surface that includesthe base, tapered, and truncated interior surfaces, the overall interiorsurface comprises aluminum, barium, beryllium, bismuth, cadmium,calcium, copper, gallium, gadolinium, germanium, lanthanum, lead,lithium, indium, mercury, molybdenum, niobium, nitrogen, osmium, oxygen,protactinium, rhenium, ruthenium, silicon, strontium, sulfur, tantalum,technetium, thallium, thorium, titanium, tin, vanadium, yttrium, zinc,zirconium, NbTi, PbMoS, V₃Ga, NbN, V₃Si, Nb₃Sn, Nb₃Al, Nb₃(AlGe), Nb₃Ge,Bi₂Sr₂CuO₆, Bi₂Sr₂CaCu₂O₈, Bi₂Sr₂Ca₂Cu₃O₁₀, YBa₂Cu₃O₇, YBa₂Cu₄O₈,Y₂Ba₄Cu₇O₁₅, Y₃Ba₅Cu₈O₁₈, Tl₂Ba₂CuO₆, Tl₂Ba₂CaCu₂O₈, Tl₂Ba₂Ca₂Cu₃O₁₀,TlBa₂Ca₃Cu₄O₁₁, HgBa₂CuO₄, HgBa₂CaCu₂O₆, HgBa₂Ca₂Cu₃O₈, or anycombination thereof.
 30. The thruster of claim 23, wherein the cavitycomprises a vacuum with a pressure between about 10{circumflex over( )}-24 Torr to about 10{circumflex over ( )}3 Torr.
 31. The thruster ofclaim 23, wherein the cavity comprises a thermal reservoir with atemperature between about 10{circumflex over ( )}-3 Kelvin to about10{circumflex over ( )}3 Kelvin.
 32. The thruster of claim 23, whereinthe electromagnetic wave comprises a transverse magnetic wave with apolar mode number of N1 and an azimuthal mode number of N2, where N1 andN2 are an integers from 0 to 1000, and N1 is greater than or equal toN2.
 33. The thruster of claim 23, wherein the electromagnetic wavecomprises a transverse magnetic wave with a polar mode number of N andan azimuthal mode number of 0, where N is an integer from 0 to
 1000. 34.The thruster of claim 23, wherein the electromagnetic wave comprises atransverse magnetic wave with a polar mode number of N and an azimuthalmode number of N, where N is an integer from 0 to
 1000. 35. The thrusterof claim 23, wherein the electromagnetic wave comprises a transverseelectric wave with a polar mode number of N1 and an azimuthal modenumber of N2, where N1 and N2 are an integers from 0 to 1000, and N1 isgreater than or equal to N2.
 36. The thruster of claim 23, wherein theelectromagnetic wave comprises a transverse electric wave with a polarmode number of N and an azimuthal mode number of 0, where N is aninteger from 0 to
 1000. 37. The thruster of claim 23, wherein theelectromagnetic wave comprises a transverse electric wave with a polarmode number of N and an azimuthal mode number of N, where N is aninteger from 0 to
 1000. 38. The thruster of claim 23, wherein theelectromagnetic radiation source is located inside the cavity at, oradjacent to, a maximum field amplitude or an asymptotic field amplitudeof the electromagnetic wave.
 39. The thruster of claim 23, wherein thecavity has at least one of a width and a height between about10{circumflex over ( )}-9 meters to about 10{circumflex over ( )}3meters.
 40. The thruster of claim 23, wherein the tapered interiorsurface forms an aperture angle between about 5 degrees to about 175degrees.
 41. The thruster of claim 23, wherein the cavity has a wallwith a wall thickness between about 10{circumflex over ( )}-9 meters toabout 1.0 meter.
 42. The thruster of claim 23, wherein the base interiorsurface is one or more of substantially elliptical, substantiallycircular, and substantially flat.
 43. The thruster of claim 23, whereinthe electromagnetic wave forms an electromagnetic energy momentum tensorwith an amplitude maximum at, or adjacent to, the base interior surface,which results in one or more of a metric tensor curvature, a thrust, andan acceleration of the thruster.
 44. The thruster of claim 23, whereinthe electromagnetic wave forms an electromagnetic energy momentum tensorwith an amplitude maximum at, or adjacent to, one or both the taperedinterior surface and the truncated interior surface, which results inone or more of a metric tensor curvature, a thrust, and an accelerationof the thruster.
 45. An electromagnetic energy momentum thrustercomprising: a) a cavity resonator forming a pyramidal cavity having abase interior surface and at least three tapered interior surfaces, thetapered interior surfaces converging to an apex point; and b) anelectromagnetic radiation source in communication with the cavityresonator, the electromagnetic radiation source configured to emit anelectromagnetic wave having a frequency between about 1.0 MHz to about1000 THz into the cavity resonator.
 46. The thruster of claim 45,wherein the electromagnetic radiation source is configured to producethe frequency of the electromagnetic wave in evanescence so that theelectromagnetic wave has a maximum field amplitude and an asymptoticfield amplitude, the maximum field amplitude being at, or adjacent to,the base interior surface, the asymptotic field amplitude being at, oradjacent to, one or more of the at least three tapered interior surfacesand the apex point.
 47. The thruster of claim 45, wherein theelectromagnetic radiation source is configured to produce the frequencyof the electromagnetic wave in evanescence so that the electromagneticwave has a maximum field amplitude and an asymptotic field amplitude,the maximum field amplitude being at, or adjacent to, one or more of theat least three tapered interior surfaces and the apex point, and theasymptotic field amplitude being at, or adjacent to, the base interiorsurface.
 48. The thruster of claim 45, wherein the cavity includes anoverall interior surface that includes the base and tapered interiorsurfaces, substantially the entire overall interior surface beingelectrically conductive, wherein the cavity resonator has a qualityfactor between about 10{circumflex over ( )}3 to about 10{circumflexover ( )}9.
 49. The thruster of claim 45, wherein the cavity includes anoverall interior surface that includes the base and tapered interiorsurfaces, the overall interior surface comprises aluminum, antimony,arsenic, barium, beryllium, bismuth, cadmium, calcium, carbon, chromium,cobalt, copper, gallium, gold, hydrogen, indium, iron, lanthanum, lead,lithium, magnesium, manganese, mercury, molybdenum, nickel, niobium,nitrogen, oxygen, palladium, phosphorus, platinum, scandium, silicon,silver, strontium, sulfur, tantalum, technetium, tin, titanium,tungsten, vanadium, yttrium, zinc, zirconium, or any combinationthereof.
 50. The thruster of claim 45, wherein the cavity includes anoverall interior surface that includes the base and tapered interiorsurfaces, substantially the entire overall interior surface beingsuperconductive, wherein the cavity resonator has a quality factorbetween about 10{circumflex over ( )}6 to about 10{circumflex over( )}15.
 51. The thruster of claim 45, wherein the cavity includes anoverall interior surface that includes the base and tapered interiorsurfaces, the overall interior surface comprises aluminum, barium,beryllium, bismuth, cadmium, calcium, copper, gallium, gadolinium,germanium, lanthanum, lead, lithium, indium, mercury, molybdenum,niobium, nitrogen, osmium, oxygen, protactinium, rhenium, ruthenium,silicon, strontium, sulfur, tantalum, technetium, thallium, thorium,titanium, tin, vanadium, yttrium, zinc, zirconium, NbTi, PbMoS, V₃Ga,NbN, V₃Si, Nb₃Sn, Nb₃Al, Nb₃(AlGe), Nb₃Ge, Bi₂Sr₂CuO₆, Bi₂Sr₂CaCu₂O₈,Bi₂Sr₂Ca₂Cu₃O₁₀, YBa₂Cu₃O₇, YBa₂Cu₄O₈, Y₂Ba₄Cu₇O₁₅, Y₃Ba₅Cu₈O₁₈,Tl₂Ba₂CuO₆, Tl₂Ba₂CaCu₂O₈, Tl₂Ba₂Ca₂Cu₃O₁₀, TlBa₂Ca₃Cu₄O₁₁, HgBa₂CuO₄,HgBa₂CaCu₂O₆, HgBa₂Ca₂Cu₃O₈, or any combination thereof.
 52. Thethruster of claim 45, wherein the cavity comprises a vacuum with apressure between about 10{circumflex over ( )}-24 Torr to about10{circumflex over ( )}3 Torr.
 53. The thruster of claim 45, wherein thecavity comprises a thermal reservoir with a temperature between about10{circumflex over ( )}-3 Kelvin to about 10{circumflex over ( )}3Kelvin.
 54. The thruster of claim 45, wherein the electromagnetic wavecomprises a transverse magnetic wave with a polar mode number of N1 andan azimuthal mode number of N2, where N1 and N2 are an integers from 0to 1000, and N1 is greater than or equal to N2.
 55. The thruster ofclaim 45, wherein the electromagnetic wave comprises a transversemagnetic wave with a polar mode number of N and an azimuthal mode numberof 0, where N is an integer from 0 to
 1000. 56. The thruster of claim45, wherein the electromagnetic wave comprises a transverse magneticwave with a polar mode number of N and an azimuthal mode number of N,where N is an integer from 0 to
 1000. 57. The thruster of claim 45,wherein the electromagnetic wave comprises a transverse electric wavewith a polar mode number of N1 and an azimuthal mode number of N2, whereN1 and N2 are an integers from 0 to 1000, and N1 is greater than orequal to N2.
 58. The thruster of claim 45, wherein the electromagneticwave comprises a transverse electric wave with a polar mode number of Nand an azimuthal mode number of 0, where N is an integer from 0 to 1000.59. The thruster of claim 45, wherein the electromagnetic wave comprisesa transverse electric wave with a polar mode number of N and anazimuthal mode number of N, where N is an integer from 0 to
 1000. 60.The thruster of claim 45, wherein the electromagnetic radiation sourceis located inside the cavity at, or adjacent to, a maximum fieldamplitude or an asymptotic field amplitude of the electromagnetic wave.61. The thruster of claim 45, wherein the cavity has at least one of awidth and a height between about 10{circumflex over ( )}-9 meters toabout 10{circumflex over ( )}3 meters.
 62. The thruster of claim 45,wherein two or more of the at least three tapered interior surfaces forman aperture angle between about 5 degrees to about 175 degrees.
 63. Thethruster of claim 45, wherein the cavity has a wall with a wallthickness between about 10{circumflex over ( )}-9 meters to about 1.0meter.
 64. The thruster of claim 45, wherein the base interior surfaceof the cavity comprises one or more of the following features: a)comprises 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,20, 21, 22, 23, or 24 sides, b) is substantially equilateral, and c) issubstantially flat.
 65. The thruster of claim 45, wherein theelectromagnetic wave forms an electromagnetic energy momentum tensorwith an amplitude maximum at, or adjacent to, the base interior surface,which results in one or more of a metric tensor curvature, a thrust, andan acceleration of the thruster.
 66. The thruster of claim 45, whereinthe electromagnetic wave forms an electromagnetic energy momentum tensorwith an amplitude maximum at, or adjacent to, one or more of the atleast three tapered interior surfaces and the apex point, which resultsin one or more of a metric tensor curvature, a thrust, and anacceleration of the thruster.
 67. An electromagnetic energy momentumthruster comprising: a) a cavity resonator forming a pyramidal cavityhaving a base interior surface, at least three tapered interiorsurfaces, and a truncated interior surface opposing the base interiorsurface, the tapered interior surfaces being between the base andtruncated interior surfaces; and b) an electromagnetic radiation sourcein communication with the cavity resonator, the electromagneticradiation source configured to emit an electromagnetic wave having afrequency between about 1.0 MHz to about 1000 THz into the cavityresonator.
 68. The thruster of claim 67, wherein the electromagneticradiation source is configured to produce the frequency of theelectromagnetic wave in evanescence so that the electromagnetic wave hasa maximum field amplitude and an asymptotic field amplitude, the maximumfield amplitude being at, or adjacent to, the base interior surface, theasymptotic field amplitude being at, or adjacent to, one or more of theat least three tapered interior surfaces and the truncated interiorsurface.
 69. The thruster of claim 67, wherein the electromagneticradiation source is configured to produce the frequency of theelectromagnetic wave in evanescence so that the electromagnetic wave hasa maximum field amplitude and an asymptotic field amplitude, the maximumfield amplitude being at, or adjacent to, one or more of the at leastthree tapered interior surfaces and the truncated interior surface, theasymptotic field amplitude being at, or adjacent to, the base interiorsurface.
 70. The thruster of claim 67, wherein the cavity includes anoverall interior surface that includes the base, tapered, and truncatedinterior surfaces, substantially the entire overall interior surfacebeing electrically conductive, wherein the cavity resonator has aquality factor between about 10{circumflex over ( )}3 to about10{circumflex over ( )}9.
 71. The thruster of claim 67, wherein thecavity includes an overall interior surface that includes the base,tapered, and truncated interior surfaces, the overall interior surfacecomprises aluminum, antimony, arsenic, barium, beryllium, bismuth,cadmium, calcium, carbon, chromium, cobalt, copper, gallium, gold,hydrogen, indium, iron, lanthanum, lead, lithium, magnesium, manganese,mercury, molybdenum, nickel, niobium, nitrogen, oxygen, palladium,phosphorus, platinum, scandium, silicon, silver, strontium, sulfur,tantalum, technetium, tin, titanium, tungsten, vanadium, yttrium, zinc,zirconium, or any combination thereof.
 72. The thruster of claim 67,wherein the cavity includes an overall interior surface that includesthe base, tapered, and truncated interior surfaces, substantially theentire overall interior surface being superconductive, wherein thecavity resonator has a quality factor between about 10{circumflex over( )}6 to about 10{circumflex over ( )}15.
 73. The thruster of claim 67,wherein the cavity includes an overall interior surface that includesthe base, tapered, and truncated interior surfaces, the overall interiorsurface comprises aluminum, barium, beryllium, bismuth, cadmium,calcium, copper, gallium, gadolinium, germanium, lanthanum, lead,lithium, indium, mercury, molybdenum, niobium, nitrogen, osmium, oxygen,protactinium, rhenium, ruthenium, silicon, strontium, sulfur, tantalum,technetium, thallium, thorium, titanium, tin, vanadium, yttrium, zinc,zirconium, NbTi, PbMoS, V₃Ga, NbN, V₃Si, Nb₃Sn, Nb₃Al, Nb₃(AlGe), Nb₃Ge,Bi₂Sr₂CuO₆, Bi₂Sr₂CaCu₂O₈, Bi₂Sr₂Ca₂Cu₃O₁₀, YBa₂Cu₃O₇, YBa₂Cu₄O₈,Y₂Ba₄Cu₇O₁₅, Y₃Ba₅Cu₈O₁₈, Tl₂Ba₂CuO₆, Tl₂Ba₂CaCu₂O₈, Tl₂Ba₂Ca₂Cu₃O₁₀,TlBa₂Ca₃Cu₄O₁₁, HgBa₂CuO₄, HgBa₂CaCu₂O₆, HgBa₂Ca₂Cu₃O₈, or anycombination thereof.
 74. The thruster of claim 67, wherein the cavitycomprises a vacuum with a pressure between about 10{circumflex over( )}-24 Torr to about 10{circumflex over ( )}3 Torr.
 75. The thruster ofclaim 67, wherein the cavity comprises a thermal reservoir with atemperature between about 10{circumflex over ( )}-3 Kelvin to about10{circumflex over ( )}3 Kelvin.
 76. The thruster of claim 67, whereinthe electromagnetic wave comprises a transverse magnetic wave with apolar mode number of N1 and an azimuthal mode number of N2, where N1 andN2 are an integers from 0 to 1000, and N1 is greater than or equal toN2.
 77. The thruster of claim 67, wherein the electromagnetic wavecomprises a transverse magnetic wave with a polar mode number of N andan azimuthal mode number of 0, where N is an integer from 0 to
 1000. 78.The thruster of claim 67, wherein the electromagnetic wave comprises atransverse magnetic wave with a polar mode number of N and an azimuthalmode number of N, where N is an integer from 0 to
 1000. 79. The thrusterof claim 67, wherein the electromagnetic wave comprises a transverseelectric wave with a polar mode number of N1 and an azimuthal modenumber of N2, where N1 and N2 are an integers from 0 to 1000, and N1 isgreater than or equal to N2.
 80. The thruster of claim 67, wherein theelectromagnetic wave comprises a transverse electric wave with a polarmode number of N and an azimuthal mode number of 0, where N is aninteger from 0 to
 1000. 81. The thruster of claim 67, wherein theelectromagnetic wave comprises a transverse electric wave with a polarmode number of N and an azimuthal mode number of N, where N is aninteger from 0 to
 1000. 82. The thruster of claim 67, wherein theelectromagnetic radiation source is located inside the cavity at, oradjacent to, a maximum field amplitude or an asymptotic field amplitudeof the electromagnetic wave.
 83. The thruster of claim 67, wherein thecavity has at least one of a width and a height between about10{circumflex over ( )}-9 meters to about 10{circumflex over ( )}3meters.
 84. The thruster of claim 67, wherein two or more of the atleast three tapered interior surfaces form an aperture angle betweenabout 5 degrees to about 175 degrees.
 85. The thruster of claim 67,wherein the cavity has a wall with a wall thickness between about10{circumflex over ( )}-9 meters to about 1.0 meter.
 86. The thruster ofclaim 67, wherein the base interior surface of the cavity comprises oneor more of the following features: a) comprises 3, 4, 5, 6, 7, 8, 9, 10,11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, or 24 sides, b) issubstantially equilateral, or c) is substantially flat.
 87. The thrusterof claim 67, wherein the electromagnetic wave forms an electromagneticenergy momentum tensor with an amplitude maximum at, or adjacent to, thebase interior surface, which results in one or more of a metric tensorcurvature, a thrust, and an acceleration of the thruster.
 88. Thethruster of claim 67, wherein the electromagnetic wave forms anelectromagnetic energy momentum tensor with an amplitude maximum at, oradjacent to, one or more of the at least three tapered interior surfacesand the truncated interior surface, which results in one or more of ametric tensor curvature, a thrust, and an acceleration of the thruster.